Question

prove that if chords of congruent circles subtend equal angles at their centre then the chords are equal​

Answer 1

Step-by-step explanation:

the angle subtended by an arc at center is double the angle subtended by it at any point on the remaining parts of circle

It is the correct statement bro

Answer 2

━━━━━━━━━━━━━━━━━━━━

$\sf\underbrace{Question:}$

• prove that if chrodes of congruent circles subtend equal angle at their centres, then the chords are equal?

$\sf\underline\red{Given:}$

• Two congruent circles $\sf C_{1}$ & $\sf C_{2}$ AB is the chord of $\sf C_{1}$& PQ is the chord of $\sf C_{2}$ & ∠AOB = ∠PXQ

$\sf\underline\orange{To\:prove:}$

• Chords are equal, i.e, AB = PQ

$\sf\underline\purple{Solution:}$

in ∆AOB & PXQ

ㅤㅤㅤㅤ$⟶$ $\sf{AO\:=\:PX}$

ㅤㅤㅤㅤ$⟶$ $\sf{∠AOB\: = \:∠PXQ}$

ㅤㅤㅤㅤ$⟶$ $\sf{BO\:=\:QX}$

ㅤㅤㅤㅤ$⟶$ $\sf{∆AOB\:≈\:∆PXQ }$

ㅤㅤㅤㅤ$⟶$ $\sf{∴\:AB\:=\:PQ }$

$\large{ \underline{ \boxed{ \textsf{∴\:AB\:=\:PQ\:(CPCT)}}}}$

━━━━━━━━━━━━━━━━━━━━