Updated on: 2026-03-31 | Author: Aarti Kulkarni

Geometry (Math 2) Chapter 4 Geometric Constructions Solutions

Q1. AB = 6 cm, ∠BAQ = 50°. Draw a circle passing through A and B so that AQ is the tangent to the circle

Diagram: Refer textbook

Q2. ∆ABC ~ ∆PBQ. In ∆ABC, AB = 3 cm, ∠B = 90°, BC = 4 cm. Ratio of the corresponding sides of two triangles is 7 : 4. Then construct ∆ABC and ∆PBQ

Diagram: Refer textbook

Q3. ΔABC ~ ΔPBR, BC = 8 cm, AC = 10 cm , ∠B = 90°, `"BC"/"BR" = 5/4` then construct ∆ABC and ΔPBR

Diagram: Refer textbook

Q4. ∆AMT ~ ∆AHE. In ∆AMT, AM = 6.3 cm, ∠TAM = 50°, AT = 5.6 cm. `"AM"/"AH" = 7/5`. Construct ∆AHE.

Diagram: Refer textbook

Q5. ΔAMT ~ ΔAHE. In ΔAMT, AM = 6.3 cm, ∠MAT = 120°, AT = 4.9 cm, `"AM"/"HA" = 7/5`, then construct ΔAMT and ΔAHE

Diagram: Refer textbook

Q6. Choose the correct alternative: ______ number of tangents can be drawn to a circle from the point on the circle.

1

Q7. Choose the correct alternative: ______ number of tangents can be drawn to a circle from the point outside the circle

2

Q8. Choose the correct alternative: ∆ABC ∼ ∆AQR. `"AB"/"AQ" = 7/5`, then which of the following option is true?

Diagram: Refer textbook

Q9. Choose the correct alternative: In the figure ΔABC ~ ΔADE then the ratio of their corresponding sides is ______

Diagram: Refer textbook

Q10. Choose the correct alternative: ΔLMN ~ ΔHIJ and `"LM"/"HI" = 2/3` then

ΔLMN is a smaller triangle

Q11. Choose the correct alternative: ΔPQR ~ ΔABC, `"PR"/"AC" = 5/7`, then

ΔABC is greater

Q12. Choose the correct alternative: The tangents drawn at the end of a diameter of a circle are ______

parallel

Q13. Choose the correct alternative: Which theorem is used while constructing a tangent to the circle by using center of a circle?

Tangent – radius theorem

Q14. Complete the following activity to draw tangents to the circle. Draw a circle with radius 3.3 cm and center O. Draw chord PQ of length 6.6 cm. Draw ray OP and ray OQ. Draw a line perpendicular to the ray OP from P. Draw a line perpendicular to the ray OQ from Q.

Diagram: Refer textbook

Q15. Construct ∠ABC = 60° and bisect it

Diagram: Refer textbook

Q16. Construct an equilateral ∆ABC with side 5 cm. ∆ABC ~ ∆LMN, ratio the corresponding sides of triangle is 6 : 7, then construct ΔLMN and ΔABC

Diagram: Refer textbook

Q17. Construct ∠PQR = 115° and divide it into two equal parts

Diagram: Refer textbook

Q18. Do the following activity to draw tangents to the circle without using the center of the circle. Draw a circle with radius 3.5 cm and take any point C on it. Draw chord CB and an inscribed angle CAB. With the center A and any convenient radius, draw an arc intersecting the sides of angle BAC in points M and N. Using the same radius, draw an arc intersecting the chord CB at point R. Taking the radius equal to d(MN) and center R, draw an arc intersecting the arc drawn in the previous step. Let D be the point of intersection of these arcs. Draw line CD. Line CD is the required tangent to the circle.

Diagram: Refer textbook

Q19. Draw a circle and take any point P on the circle. Draw ray OP ↓ Draw perpendicular to ray OP from point P

Diagram: Refer textbook

Q20. Draw a circle of radius 3 cm and draw a tangent to the circle from point P on the circle

Diagram: Refer textbook

Q21. Draw a circle of radius 3 cm and draw chord XY 5 cm long. Draw the tangent of the circle passing through point X and point Y (without using the center of the circle)

Diagram: Refer textbook

Q22. Draw a circle of radius 3 cm. Take any point K on it. Draw a tangent to the circle from point K without using center of the circle.

Diagram: Refer textbook

Q23. Draw a circle of radius 3.4 cm. Draw a chord MN 5.7 cm long in a circle. Draw a tangent to the circle from point M and point N

Diagram: Refer textbook

Q24. Draw a circle of radius 3.4 cm, take any point P on it. Draw tangent to the circle from point P

Diagram: Refer textbook

Q25. Draw a circle of radius 4.2 cm. Draw a tangent to the circle at point P on the circle without using the center of the circle

Diagram: Refer textbook

Q26. Draw a circle of radius 4.2 cm. Draw a tangent to the circle from a point 7 cm away from the center of the circle

Diagram: Refer textbook

Q27. Draw a circle of radius 4.2 cm. Draw arc PQ measuring 120°. Draw a tangent to the circle from point P and point Q

Diagram: Refer textbook

Q28. Draw a circle of radius 4.2 cm, take any point M on it. Draw tangent to the circle from point M

Diagram: Refer textbook

Q29. Draw a circle with a diameter AB of length 6 cm. Draw a tangent to the circle from the end points of the diameter.

Diagram: Refer textbook

Q30. Draw a circle with a radius of 3.3 cm. Draw a chord PQ of length 6.6 cm. Draw tangents to the circle at points P and Q. Write your observation about the tangents.

Answer

Diagram: Refer textbook

Q31. Draw a circle with a radius of 3.5 cm. Take the point K anywhere on the circle. Draw a tangent to the circle from K (without using the center of the circle)

Diagram: Refer textbook

Q32. Draw a circle with center C and radius 3.2 cm. Draw a tangent to the circle from point P at a distance of 7.5 cm from the center of the circle

Diagram: Refer textbook

Q33. Draw a circle with center O and radius 2.8 cm. Take point P in the exterior of a circle such that tangents PA and PB drawn from point P make an angle ∠APB of measure 70°

Diagram: Refer textbook

Q34. Draw a circle with center O and radius 3 cm ↓ Take any point P on the circle ↓ Draw ray OP ↓ Draw perpendicular to ray OP from point P

Diagram: Refer textbook

Q35. Draw a circle with center O and radius 3 cm. Take point P outside the circle such that d (O, P) = 4.5 cm. Draw tangents to the circle from point P.

Diagram: Refer textbook

Q36. Draw a circle with center O and radius 3 cm. Take the point P and the point Q at a distance of 7 cm from the center of the circle on the opposite side of the circle such that their line of intersection passing through the center of the circle Draw a tangent to the circle from the point P and the point Q

Diagram: Refer textbook

Q37. Draw a circle with center O and radius 3.4. Draw a chord MN of length 5.7 cm in a circle. Draw tangents to the circle from point M and N

Diagram: Refer textbook

Q38. Draw a circle with center O and radius 3.6 cm. Draw a tangent to the circle from point B at a distance of 7.2 cm from the center of the circle.

Diagram: Refer textbook

Q39. Draw a circle with center P. Draw an arc AB of 100° measure. Perform the following steps to draw tangents to the circle from points A and B. Draw a circle with any radius and center P. Take any point A on the circle. Draw ray PB such ∠APB = 100°. Draw perpendicular to ray PA from point A. Draw perpendicular to ray PB from point B.

Diagram: Refer textbook

Q40. Draw a circle with radius 3 cm. Construct a square such that each of its side will touch the circle from outside

Diagram: Refer textbook

Q41. Draw a circle with radius 4 cm and construct two tangents to a circle such that when those two tangents intersect each other outside the circle they make an angle of 60° with each other

Diagram: Refer textbook

Q42. Draw any circle with radius greater than 1.8 cm and less than 3 cm. Draw a chord AB 3.6 cm long in this circle. Tangent to the circle passing through A and B without using the center of the circle

Diagram: Refer textbook

Q43. Draw seg AB = 6.8 cm. Draw a circle with diameter AB. Draw point C on the circle apart from A and B. Draw line AC and line CB. Write the measure of angle ACB

Answer

Diagram: Refer textbook

Q44. Draw seg AB of length 4.5 cm and draw its perpendicular bisector

Diagram: Refer textbook

Q45. Draw seg AB of length 9 cm and divide it in the ratio 3 : 2

Diagram: Refer textbook

Q46. Draw Seg AB of length 9.7 cm. Take point P on it such that AP = 3.5 cm and A–P–B. Construct perpendicular to seg AB from point P.

Diagram: Refer textbook

Q47. Point P is at a distance of 6 cm from line AB. Draw a circle of radius 4 cm passing through point P so that line AB is the tangent to the circle

Diagram: Refer textbook

Q48. ΔPQR ~ ΔABC. In ΔPQR, PQ = 3.6cm, QR = 4 cm, PR = 4.2 cm. Ratio of the corresponding sides of triangle is 3 : 4, then construct ΔPQR and ΔABC

Diagram: Refer textbook

Q49. ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm, ∠D = 30°, ∠N = 20° and `"HP"/"ED" = 4/5`. Then construct ΔRHP and ΔNED

Diagram: Refer textbook

Q50. ΔRHP ~ ΔNED, In ΔNED, NE = 7 cm. ∠D = 30°, ∠N = 20°, `"HP"/"ED" = 4/5`, then construct ΔRHP and ∆NED

Diagram: Refer textbook

Q51. Take point P and Q and draw a circle passing through them. Draw a tangent AB to the circle without using the centre of the circle.

Diagram: Refer textbook

Q52. To draw tangents to the circle from the endpoints of the diameter of the circle. Construct a circle with center O. Draw any diameter AB of it ↓ Draw ray OA and ray OB ↓ Construct perpendicular to ray OA from point A ↓ Construct perpendicular to Ray OB from point B

Diagram: Refer textbook

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