# In Fig. 10.36, A, B and C are three points on a circle with centre O such that ∠BOC = 30º and ∠AOB = 60º. If D is a point on the circle other than the arc ABC, find ∠ADC.

**Solution:**

The angle subtended by an arc at the center is double the angle subtended by it at any point on the remaining part of the circle.

∠AOC = ∠AOB + ∠BOC = 90°

∠AOC = 2 ∠ADC (By Theorem 10.8)

∠ADC = 1/2 ∠AOC

∠ADC = 1/2 × 90 = 45°

∴ ∠ADC = 45°

**Video Solution:**

## In Fig. 10.36, A, B and C are three points on a circle with center O such that ∠BOC = 30º and ∠AOB = 60º. If D is a point on the circle other than the arc ABC, find ∠ADC.

### Maths NCERT Solutions Class 9 - Chapter 10 Exercise 10.5 Question 1:

**Summary:**

If, in the given figure, A, B, and C are three points on a circle with center O such that ∠BOC = 30° and ∠AOB = 60°, D is a point on the circle other than the arc ABC, then ∠ADC = 45°.