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# 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°.

**☛ Check: **NCERT Solutions for Class 10 Maths Chapter 11

**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

**Summary:**

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°.

**☛ Related Questions:**

- Draw a circle of radius 6 cm. From a point 10 cm away from its centre, construct the pair of tangents to the circle and measure their lengths.
- Construct a tangent to a circle of radius 4 cm from a point on the concentric circle of radius 6 cm and measure its length. Also, verify the measurement by actual calculation.
- Draw a circle of radius 3 cm. Take two points P and Q on one of its extended diameters each at a distance of 7 cm from its centre. Draw tangents to the circle from these two points P and Q.

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