# Draw a pair of tangents to a circle of radius 5 cm which is inclined to each other at an angle of 60°

**Solution:**

Steps of construction:

- With O as the centre and 5cm as radius draw a circle.
- Take a point A on the circumference of the circle and join OA.
- Draw AX perpendicular to OA.
- Construct ∠AOB = 120° where B lies on the circumference.
- Draw BY perpendicular to OB.
- Both AX and BY intersect at P.
- PA and PB are the required tangents inclined at 60°.

Proof:

∠OAP = ∠OBP = 90° (By construction)

∠AOB = 120° (By construction)

In quadrilateral OAPB,

∠APB = 360° - [∠OAP + ∠OBP + ∠AOB]

= 360° - [90° + 90° + 120°]

= 360° - 300°

= 60°

Hence PA and PB are the required tangents inclined at 60°.

**Video Solution:**

## Draw a pair of tangents to a circle of radius 5 cm which is inclined to each other at an angle of 60°

### NCERT Solutions Class 10 Maths - Chapter 11 Exercise 11.2 Question 4:

Draw a pair of tangents to a circle of radius 5 cm which is inclined to each other at an angle of 60°

PA and PB are the required tangents to a circle of radius 5 cm which are inclined to each other at an angle of 60°