Question

PT Angles in the same segment of a circle are equal.​

Answer 1

Theorem :-

" Angles in the same segment of a circle are equal".

Given :-

The centre of a circle is O.

AB is a chord.

∠ACB and ∠ADB are the angled in the same segment according to the chord AB.

Required To Prove :-

∠ACB = ∠ADB

Construction :-

Join OA and OB

Proof :-

AB is a chord .

C is the point remaining part of the circle.

We know that

" The angle subtended by an arc at the centre is twice the angle subtended by it at any point in the remaining part of the circle".

∠AOB = 2 ∠ACB ----------(1)

∠AOB = 2 ∠ADB ----------(2)

From (1)&(2)

2 ∠ACB = 2 ∠ADB

=> ∠ ACB = ∠ ADB

" Angles in the same segment of a circle are equal".

Hence, Proved.