Question

Help me in this question pls :-

⭐ Prove that if chords of congruent circles subtend equal angles at their centres, then the chords are equal.

I need answer from mods or stars ✅✅​

Answer 1

Given:- Two congruent circles $\sf{{C}_{1}}$ and $\sf{{C}_{2}}$. AB is the chord of $\sf{{C}_{1}}$ and PQ is the chord of $\sf{{C}_{2}}$. ∠AOB = ∠PXQ.

‎‎

To Prove:- AB = PQ

‎

Proof:- In ∆AOB and ∆PXQ

‎

$\rightarrow$ AO = PX.. .. .. [Radius of congruent circle are equal]

$\rightarrow$ ∠AOB = ∠PXQ.. .. .. [Given]

$\rightarrow$ OB = XQ.. .. .. [Radius of congruent circle are equal]

‎

‎∴ ∆AOB ≅ ∆PXQ

∴ AB = PB.. .. .. [By CPCT (Congruent part of congruent triangles)]

$\large{\underline{Hence\:Proved}}$