Question

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

Answer 1

Here is your answer ☺️☺️❤️❤️

So in the given figure :

In triangle ABO and PQO

OA = OP (Radii)

Angld AOB = Angle PoQ (given)

OB = OQ (radii)

By SAS

Triangle ABO is congruent to PQO

By CPCT

AB = PQ

Hence proved.

Hope this helps you ☺️☺️❤️❤️

Answer 2

Given:

Two circles with centres O and O’

AB = PQ

To prove:

∠AOB = ∠PO’Q

Proof:

In ΔAOB and ΔPO’Q

AB = PQ (Given)

OA = O’P (Radii)

OB=O’Q (Radii)

Hence ΔAOB ≅ ΔPO’Q [By SSS Congruence property]

⇒ ∠AOB = ∠PO’Q [CPCT]

HENCE PROVED!!!!