100 Constructions Questions for Class 10 Maths with NCERT Book Solutions
Master Constructions for Class 10 Maths with 100 practice questions and NCERT book solutions, covering division of line segments, triangles, and tangents. Sourced from CBSE Board Exams (2015–2024), NTSE, IMO, and original questions, these copyright-free questions are ideal for 2025 board and competitive exam preparation. Download the free PDF!
Access official resources at NCERT or CBSE for past papers and study materials.
Table of Contents
Questions 1–34
1. Divide a line segment of length 6 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle from A. 3. Mark 5 points (2+3) A1, A2, A3, A4, A5 on AX at equal intervals using a compass. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
2. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm using a ruler and compass. 2. Draw ray BX downward from B. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
3. Draw a circle of radius 4 cm and construct a tangent to it from a point 10 cm away from the center. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P, 10 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
4. Divide a line segment of 8 cm in the ratio 3:2 internally. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 5 points (3+2) A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A3, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 3:2 (AC:CB = 3:2).
5. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 3/4. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX at equal intervals. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
6. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass (set compass to any radius, mark arcs above and below P, find midpoint of arcs to draw perpendicular). The line through P is the tangent.
7. Divide a line segment of 10 cm in the ratio 1:2 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 3 points (1+2) A1, A2, A3 on AX at equal intervals. 4. Join A3B. 5. From A1, draw a line parallel to A3B intersecting AB at C. Point C divides AB in the ratio 1:2 (AC:CB = 1:2).
8. Construct a triangle with sides 3 cm, 4 cm, and 5 cm, then construct a triangle similar to it with a scale factor of 2/5. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 3 cm, BC = 4 cm, CA = 5 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX at equal intervals. 4. Join B5C. 5. From B2, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/5.
9. Draw a circle of radius 5 cm and construct two tangents from a point 12 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 5 cm. 2. Mark point P, 12 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
10. Divide a line segment of 7 cm in the ratio 3:4 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 7 cm. 2. Draw ray AX at any angle. 3. Mark 7 points (3+4) A1, A2, A3, A4, A5, A6, A7 on AX at equal intervals. 4. Join A7B. 5. From A3, draw a line parallel to A7B intersecting AB at C. Point C divides AB in the ratio 3:4 (AC:CB = 3:4).
11. Construct a triangle with sides 6 cm, 7 cm, and 8 cm, then construct a triangle similar to it with a scale factor of 4/5. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 6 cm, BC = 7 cm, CA = 8 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX at equal intervals. 4. Join B5C. 5. From B4, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 4/5.
12. Draw a circle of radius 3.5 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3.5 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
13. Divide a line segment of 9 cm in the ratio 2:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 9 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
14. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/5. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX. 4. Join B5C. 5. From B3, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/5.
15. Draw a circle of radius 4.5 cm and construct two tangents from a point 11 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4.5 cm. 2. Mark point P, 11 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
16. Divide a line segment of 12 cm in the ratio 3:5 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 12 cm. 2. Draw ray AX at any angle. 3. Mark 8 points (3+5) A1, A2, A3, A4, A5, A6, A7, A8 on AX at equal intervals. 4. Join A8B. 5. From A3, draw a line parallel to A8B intersecting AB at C. Point C divides AB in the ratio 3:5 (AC:CB = 3:5).
17. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
18. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
19. Divide a line segment of 8 cm in the ratio 1:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 4 points (1+3) A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
20. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 4/5. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX. 4. Join B5C. 5. From B4, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 4/5.
21. Draw a circle of radius 5 cm and construct two tangents from a point 13 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 5 cm. 2. Mark point P, 13 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
22. Divide a line segment of 10 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
23. Construct a triangle with sides 3 cm, 4 cm, and 5 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 3 cm, BC = 4 cm, CA = 5 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
24. Draw a circle of radius 4 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
25. Divide a line segment of 6 cm in the ratio 1:2 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 3 points A1, A2, A3 on AX at equal intervals. 4. Join A3B. 5. From A1, draw a line parallel to A3B intersecting AB at C. Point C divides AB in the ratio 1:2 (AC:CB = 1:2).
26. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/5. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX. 4. Join B5C. 5. From B2, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/5.
27. Draw a circle of radius 3.5 cm and construct two tangents from a point 10 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3.5 cm. 2. Mark point P, 10 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
28. Divide a line segment of 8 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
29. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
30. Draw a circle of radius 4 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
31. Divide a line segment of 10 cm in the ratio 3:2 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A3, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 3:2 (AC:CB = 3:2).
32. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
33. Draw a circle of radius 5 cm and construct two tangents from a point 12 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 5 cm. 2. Mark point P, 12 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
34. Divide a line segment of 6 cm in the ratio 1:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
Questions 35–67
35. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/5. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX. 4. Join B5C. 5. From B3, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/5.
36. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
37. Divide a line segment of 8 cm in the ratio 2:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
38. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 4/5. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX. 4. Join B5C. 5. From B4, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 4/5.
39. Draw a circle of radius 4.5 cm and construct two tangents from a point 11 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4.5 cm. 2. Mark point P, 11 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
40. Divide a line segment of 10 cm in the ratio 3:4 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 7 points A1, A2, A3, A4, A5, A6, A7 on AX at equal intervals. 4. Join A7B. 5. From A3, draw a line parallel to A7B intersecting AB at C. Point C divides AB in the ratio 3:4 (AC:CB = 3:4).
41. Construct a triangle with sides 3 cm, 4 cm, and 5 cm, then construct a triangle similar to it with a scale factor of 2/3. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 3 cm, BC = 4 cm, CA = 5 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
42. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
43. Divide a line segment of 6 cm in the ratio 1:2 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 3 points A1, A2, A3 on AX at equal intervals. 4. Join A3B. 5. From A1, draw a line parallel to A3B intersecting AB at C. Point C divides AB in the ratio 1:2 (AC:CB = 1:2).
44. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 3/4. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
45. Draw a circle of radius 5 cm and construct two tangents from a point 13 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 5 cm. 2. Mark point P, 13 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
46. Divide a line segment of 8 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
47. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 2/3. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
48. Draw a circle of radius 3.5 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3.5 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
49. Divide a line segment of 10 cm in the ratio 1:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
50. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 3/5. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX. 4. Join B5C. 5. From B3, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/5.
51. Draw a circle of radius 4 cm and construct two tangents from a point 10 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P, 10 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
52. Divide a line segment of 6 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
53. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 4/5. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX. 4. Join B5C. 5. From B4, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 4/5.
54. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
55. Divide a line segment of 8 cm in the ratio 1:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
56. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
57. Draw a circle of radius 4.5 cm and construct two tangents from a point 11 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4.5 cm. 2. Mark point P, 11 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
58. Divide a line segment of 10 cm in the ratio 3:2 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A3, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 3:2 (AC:CB = 3:2).
59. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
60. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
61. Divide a line segment of 8 cm in the ratio 1:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
62. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
63. Draw a circle of radius 5 cm and construct two tangents from a point 13 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 5 cm. 2. Mark point P, 13 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
64. Divide a line segment of 6 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
65. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
66. Draw a circle of radius 3.5 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3.5 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
67. Divide a line segment of 8 cm in the ratio 1:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
Questions 68–100
68. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
69. Draw a circle of radius 4 cm and construct two tangents from a point 10 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P, 10 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
70. Divide a line segment of 6 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
71. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
72. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
73. Divide a line segment of 8 cm in the ratio 1:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
74. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
75. Draw a circle of radius 4.5 cm and construct two tangents from a point 11 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4.5 cm. 2. Mark point P, 11 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
76. Divide a line segment of 10 cm in the ratio 3:2 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A3, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 3:2 (AC:CB = 3:2).
77. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX. 4.Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
78. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass (set compass to any radius, mark arcs above and below P, find midpoint of arcs to draw perpendicular). The line through P is the tangent.
79. Divide a line segment of 7 cm in the ratio 2:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 7 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
80. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/5. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX at equal intervals. 4. Join B5C. 5. From B2, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/5.
81. Draw a circle of radius 4 cm and construct two tangents from a point 10 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P, 10 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
82. Divide a line segment of 9 cm in the ratio 1:2 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 9 cm. 2. Draw ray AX at any angle. 3. Mark 3 points A1, A2, A3 on AX at equal intervals. 4. Join A3B. 5. From A1, draw a line parallel to A3B intersecting AB at C. Point C divides AB in the ratio 1:2 (AC:CB = 1:2).
83. Construct a triangle with sides 3 cm, 4 cm, and 5 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 3 cm, BC = 4 cm, CA = 5 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX at equal intervals. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
84. Draw a circle of radius 3.5 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3.5 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
85. Divide a line segment of 8 cm in the ratio 3:2 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A3, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 3:2 (AC:CB = 3:2).
86. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
87. Draw a circle of radius 4 cm and construct two tangents from a point 12 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P, 12 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
88. Divide a line segment of 10 cm in the ratio 1:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
89. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/5. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 5 points B1, B2, B3, B4, B5 on BX at equal intervals. 4. Join B5C. 5. From B3, draw a line parallel to B5C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/5.
90. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
91. Divide a line segment of 6 cm in the ratio 2:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
92. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
93. Draw a circle of radius 4.5 cm and construct two tangents from a point 11 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4.5 cm. 2. Mark point P, 11 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
94. Divide a line segment of 8 cm in the ratio 3:2 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 8 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A3, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 3:2 (AC:CB = 3:2).
95. Construct a triangle with sides 4 cm, 5 cm, and 6 cm, then construct a triangle similar to it with a scale factor of 3/4. (CBSE 2018)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 4 cm, BC = 5 cm, CA = 6 cm. 2. Draw ray BX downward. 3. Mark 4 points B1, B2, B3, B4 on BX at equal intervals. 4. Join B4C. 5. From B3, draw a line parallel to B4C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 3/4.
96. Draw a circle of radius 3 cm and construct a tangent at a point P on the circle. (NCERT 11.2)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 3 cm. 2. Mark point P on the circle. 3. Draw radius OP. 4. At P, construct a perpendicular to OP using a compass. The line through P is the tangent.
97. Divide a line segment of 10 cm in the ratio 1:3 internally. (CBSE 2019)
Answer: Constructed.
Solution: 1. Draw AB = 10 cm. 2. Draw ray AX at any angle. 3. Mark 4 points A1, A2, A3, A4 on AX at equal intervals. 4. Join A4B. 5. From A1, draw a line parallel to A4B intersecting AB at C. Point C divides AB in the ratio 1:3 (AC:CB = 1:3).
98. Construct a triangle with sides 5 cm, 6 cm, and 7 cm, then construct a triangle similar to it with a scale factor of 2/3. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw ΔABC with AB = 5 cm, BC = 6 cm, CA = 7 cm. 2. Draw ray BX downward. 3. Mark 3 points B1, B2, B3 on BX at equal intervals. 4. Join B3C. 5. From B2, draw a line parallel to B3C intersecting BC at C’. 6. From C’, draw a line parallel to CA intersecting AB at A’. ΔA’BC’ is similar to ΔABC with scale factor 2/3.
99. Draw a circle of radius 4 cm and construct two tangents from a point 10 cm from the center. (CBSE 2020)
Answer: Constructed.
Solution: 1. Draw a circle with center O, radius 4 cm. 2. Mark point P, 10 cm from O. 3. Draw segment OP. 4. Find midpoint M of OP by constructing its perpendicular bisector. 5. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. 6. Draw lines PT and PT’. These are the tangents from P.
100. Divide a line segment of 6 cm in the ratio 2:3 internally. (NCERT 11.1)
Answer: Constructed.
Solution: 1. Draw AB = 6 cm. 2. Draw ray AX at any angle. 3. Mark 5 points A1, A2, A3, A4, A5 on AX at equal intervals. 4. Join A5B. 5. From A2, draw a line parallel to A5B intersecting AB at C. Point C divides AB in the ratio 2:3 (AC:CB = 2:3).
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Frequently Asked Questions
What tools are needed for geometric constructions in Class 10?
A ruler and a compass are the primary tools required for geometric constructions in Class 10, as per the NCERT syllabus. These are used to draw accurate lines, circles, and angles.
How do you divide a line segment in a given ratio?
To divide a line segment AB in the ratio m:n, draw a ray AX, mark m+n equal points on AX, join the last point to B, and draw a line parallel to this from the m-th point to intersect AB at C, dividing it in the ratio m:n.
How do you construct a tangent to a circle from an external point?
Draw a circle with center O and radius r. Mark an external point P. Join OP, find its midpoint M by constructing the perpendicular bisector. With M as center and MO as radius, draw a circle intersecting the original circle at T and T’. Lines PT and PT’ are the tangents.
What is the scale factor in similar triangle constructions?
The scale factor is the ratio of the corresponding sides of the constructed triangle to the original triangle (e.g., k = 2/3 means the new triangle’s sides are 2/3 of the original).
Why is a compass used in constructions?
A compass ensures precision in drawing arcs, circles, and equal lengths, maintaining geometric accuracy without relying on measurements alone.
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![Edit Post Button Logo Design Library Ctrl+K Save draft 17 / 100 0 / 100 Publish UP TGT PGT EXAM DATE |यूपी टीजीटी पीजीटी परीक्षा 2025: स्थगन अपडेट, नया परीक्षा कार्यक्रम और तैयारी टिप्स This image has an empty alt attribute; its file name is 20250529_223018-1024x576.jpg यूपी टीजीटी पीजीटी परीक्षा 2025: नवीनतम अपडेट और स्थगन की खबरें उत्तर प्रदेश माध्यमिक शिक्षा सेवा चयन बोर्ड (UPSESSB) द्वारा आयोजित होने वाली यूपी टीजीटी (Trained Graduate Teacher) और पीजीटी (Post Graduate Teacher) परीक्षा 2025 को लेकर अभ्यर्थियों में काफी उत्सुकता और संशय बना हुआ है। हाल के अपडेट्स के अनुसार, परीक्षा तिथियों में बदलाव की खबरें सामने आ रही हैं, जिसने अभ्यर्थियों के बीच चर्चा का माहौल बना दिया है। इस लेख में हम यूपी टीजीटी और पीजीटी परीक्षा 2025 के नवीनतम अपडेट्स, संभावित स्थगन, नया परीक्षा कार्यक्रम, और प्रभावी तैयारी टिप्स पर विस्तार से चर्चा करेंगे। यूपी टीजीटी पीजीटी परीक्षा 2025: नया परीक्षा कार्यक्रम आधिकारिक सूत्रों के अनुसार, यूपी टीजीटी और पीजीटी परीक्षा 2025 की तिथियां इस प्रकार थीं: हालांकि, हाल के अपडेट्स और सोशल मीडिया पर चल रही चर्चाओं के आधार पर, यह दावा किया जा रहा है कि यूपी पीजीटी परीक्षा 18 और 19 जून, 2025 को नहीं होगी, और यूपी टीजीटी परीक्षा भी 21 और 22 जुलाई, 2025 को स्थगित हो सकती है। इन दावों के अनुसार, दोनों परीक्षाएं अब अगस्त या सितंबर 2025 में आयोजित हो सकती हैं। यह जानकारी अनौपचारिक स्रोतों से प्राप्त हुई है और UPSESSB द्वारा अभी तक इसकी आधिकारिक पुष्टि नहीं की गई है। UPSESSB की आधिकारिक वेबसाइट upsessb.pariksha.nic.in के अनुसार, टीजीटी परीक्षा अब 21 और 22 जुलाई, 2025 को निर्धारित है, जबकि पीजीटी परीक्षा 18 और 19 जून, 2025 को होने की संभावना है। हालांकि, अनौपचारिक स्रोतों का कहना है कि ये तिथियां भी बदल सकती हैं, और परीक्षाएं अगस्त या सितंबर 2025 में हो सकती हैं। अभ्यर्थियों को सलाह दी जाती है कि वे आधिकारिक वेबसाइट पर नजर रखें, जहां जल्द ही स्थगन से संबंधित नोटिस जारी हो सकता है। परीक्षा केंद्र और एडमिट कार्ड की जानकारी फिलहाल, UPSESSB ने टीजीटी और पीजीटी परीक्षा 2025 के लिए परीक्षा केंद्रों की जानकारी जारी नहीं की है। आमतौर पर, एडमिट कार्ड के साथ परीक्षा केंद्रों की जानकारी दी जाती है, जो परीक्षा से 7-10 दिन पहले उपलब्ध होती है। अनुमानित तिथियां इस प्रकार हैं: एडमिट कार्ड डाउनलोड करने के लिए निम्नलिखित कदम उठाएं: अभ्यर्थियों को सलाह दी जाती है कि वे अपने एडमिट कार्ड को परीक्षा केंद्र पर अवश्य लाएं, क्योंकि बिना इसके प्रवेश की अनुमति नहीं होगी। पेपर लीक की आशंका और स्थगन का कारण सोशल मीडिया और कुछ अनौपचारिक स्रोतों पर दावा किया जा रहा है कि यूपी टीजीटी और पीजीटी परीक्षा 2025 के प्रश्न पत्र लीक होने की आशंका के कारण स्थगित हो सकती हैं। यह दावा किया गया है कि UPSESSB को प्रश्न पत्रों की गोपनीयता को लेकर संदेह है, जिसके कारण परीक्षा को अगस्त या सितंबर 2025 तक टाला जा सकता है। हालांकि, यह जानकारी आधिकारिक रूप से सत्यापित नहीं है। पिछले उदाहरणों, जैसे कि 2024 में बिहार लोक सेवा आयोग (BPSC) की TRE 3.0 प्राइमरी परीक्षा के पेपर लीक होने के कारण रद्द होने की घटना, से इस तरह की आशंकाओं को बल मिलता है। फिर भी, अभ्यर्थियों को सलाह दी जाती है कि वे ऐसी अफवाहों पर ध्यान न दें और केवल UPSESSB की आधिकारिक वेबसाइट से जानकारी लें। यूपी टीजीटी पीजीटी 2025: महत्वपूर्ण जानकारी यूपी टीजीटी और पीजीटी परीक्षा 2025 के माध्यम से उत्तर प्रदेश के स्कूलों में कुल 4,163 रिक्तियां भरी जाएंगी, जिनमें शामिल हैं: परीक्षा पैटर्न चयन प्रक्रिया पात्रता मानदंड यूपी टीजीटी पीजीटी 2025 के लिए SEO-अनुकूलित तैयारी टिप्स परीक्षा तिथियों में संभावित बदलाव के बावजूद, अभ्यर्थियों को अपनी तैयारी में कोई ढिलाई नहीं बरतनी चाहिए। सीमित रिक्तियों (कुल 4,163) के कारण प्रतिस्पर्धा बहुत अधिक है। यहाँ कुछ प्रभावी तैयारी टिप्स दिए गए हैं: परीक्षा स्थगन और पेपर लीक की अफवाहों पर क्या करें? सोशल मीडिया पर चल रही चर्चाओं में दावा किया गया है कि यूपी टीजीटी और पीजीटी परीक्षा 2025 को पेपर लीक की आशंका और प्रशासनिक समस्याओं, जैसे परीक्षा केंद्रों का निर्धारण न हो पाना, के कारण स्थगित किया जा सकता है। यह भी कहा गया है कि आयोग प्रयागराज में धरना-प्रदर्शन और अन्य समस्याओं से जूझ रहा है। हालांकि, एक हालिया X पोस्ट में दावा किया गया कि पीजीटी परीक्षा निर्धारित तिथियों पर ही होगी, और आयोग तिथियों को बढ़ाने के पक्ष में नहीं है। इन विरोधाभासी दावों के बीच, अभ्यर्थियों को निम्नलिखित कदम उठाने चाहिए: निष्कर्ष यूपी टीजीटी और पीजीटी परीक्षा 2025 उत्तर प्रदेश में शिक्षक बनने का सुनहरा अवसर है, जिसमें कुल 4,163 रिक्तियां भरी जाएंगी। हालांकि, अनौपचारिक स्रोतों के अनुसार, परीक्षा 18-19 जून और 21-22 जुलाई को होने की बजाय अगस्त या सितंबर 2025 में हो सकती है। यह दावा अभी सत्यापित नहीं है, और अभ्यर्थियों को आधिकारिक नोटिस का इंतजार करना चाहिए। परीक्षा की तारीखों में अनिश्चितता के बावजूद, अभ्यर्थियों को अपनी तैयारी में कोई कमी नहीं लानी चाहिए। एक संरचित अध्ययन योजना, नियमित मॉक टेस्ट, और आधिकारिक अपडेट्स पर नजर रखकर आप अपनी सफलता की संभावनाओं को बढ़ा सकते हैं। नवीनतम जानकारी के लिए upsessb.pariksha.nic.in पर नियमित रूप से जांच करें और मेहनत के साथ अपने सपनों को साकार करें! डिस्क्लेमर: परीक्षा स्थगन और पेपर लीक से संबंधित जानकारी सोशल मीडिया और अनौपचारिक स्रोतों पर आधारित है। सटीक और नवीनतम जानकारी के लिए हमेशा UPSESSB की आधिकारिक वेबसाइट देखें। Move upMove downToggle panel: Post Settings General Smart List Reviews Autoload Options Locker Post template:? 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Open publish panel Post NotificationsDrag and drop an image, upload, or choose from your library.](https://theartnews.in/wp-content/uploads/al_opt_content/IMAGE/theartnews.in/wp-content/uploads/2025/05/20250529_223018-100x70.jpg?bv_host=theartnews.in&bv-resized-infos=bv_resized_mobile%3A100%2A70%3Bbv_resized_ipad%3A100%2A70%3Bbv_resized_desktop%3A100%2A70 "UP TGT PGT EXAM DATE |यूपी टीजीटी पीजीटी परीक्षा 2025: स्थगन अपडेट, नया परीक्षा कार्यक्रम और तैयारी टिप्स")
