Given an are `PQ` of a circle subtending angles `POQ` at the centre `PAQ` at a point A on the remaining part of the circle. We need to prove that `anglePOQ=2 anglePAQ.`

Prove Equal chords of a circle subtend equal angles at the centre.

Prove that equal chords of a circle subtend equal angles at the centre.

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

Prove Equal chords of congruent circles subtend equal angles at the centre.

Theorem 10.8 : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

Theorem 10.8 : The angle subtended by an arc at the centre is double the angle subtended by it at any point on the remaining part of the circle.

(A) Choose the correct alternative : O is a centre of a circle, Tangents TP and TQ of the circles itersect at point T in the exterior of the circle. Points P and Q lie on the circle . If anglePOQ = 120^(@) then angle PTQ = ?

In figure if PR is tangent to the circle at P and O is the centre of the circle then angle POQ is