Question

Recall that two circles are congruent if they have the same radii. Prove that equal
chords of congruent circles subtend equal angles at their centres.
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Answer 1

Step-by-step explanation:

Given:- C(O,r) and C₁(O₁,r₁), where r=r₁ and PQ=AB

To prove:- ∠AOB=∠PO₁Q

Solution:- In ΔAOB and ΔPO₁Q,

                                             AB=PQ(given)

                                             AO=PO₁(since radii are equal)

                                             OB=O₁Q(")

⇒ΔAOB≅ΔPO₁Q

∴ By CPCT, ∠AOB=∠PO₁Q