Question

Theorem 10.1 : Equal chords of a circle subtend equal angles at the centre? any can explain this theorem?

Answer 1

Question

Theorem 10.1 : Equal chords of a circle subtend equal angles at the centre? any can explain this theorem?

Answer

This theorem States that, if there are 2 equal chords in a circle, the angles formed by the equal chords at the centre of the circle are equal.

Given

AB and CD are two equal chords in a circle with centre O.

To Prove

∠AOB = ∠COD

Proof

Consider ΔAOB and ΔCOD

AO = OC [radii of the same circle]

BO = OD [radii of the same circle]

AB = CD [Given]

∴ ΔAOB ≅ ΔCOD by SSS congruency.

$\implies$  ∠AOB = ∠COD [CPCT]

Hence Proved!