In Fig. 10.36, A,B and C are three points on a circle with centre O such that `\ /_B O C=\ 30^o` and `\ /_A O B =\ 60^o`. If D is a point on the circle other than the arc ABC, find `/_A D Cdot`

Explanation

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.

`angleAOC = angleAOB + angleBOC = 90^@`

`angleAOC = 2 angleADC` (By Theorem 10.8)

`angleADC = 1/2 angleAOC`

`angleADC = 1/2 xx 90 = 45^@`

`∠ADC = 45^@`