Question

prove that equal chords of a circle subtend equal angles at the centre

Answer 1

make 2 chord on a circle AB and CD equal to each other
and join them to the center O

now,. AO =CO
BO = DO. (radii of the same circle)
AB = CD. (given)
=> ∆ AOB≈ ∆ COD (by S.S.S. congruency rule)
=> angle AOB = angle COD
.•., equal chords subtends equal angles at the centre.
Hence Proved.

may this helps u

Answer 2

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

Given : AB and CD are chords of a circle with centre O, such that AB = CD.

To prove : ∠AOC = ∠COD

Proof :

In ΔAOB and ΔCOD,

AO = CO [radii of same circle]
BO = DO [radii of same circle]
AB = CD [given]

ΔAOB ≅ ΔCOD [SSS]
∠AOB = ∠COD [C. P. C. T]

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