Question

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

Question ::-

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

Given ::-

• Radii of two circles are equal.

• AB = DE

• AC = DF

• BC = EF

To find ::-

• ∠A = ∠D

Solution ::-

by SSS congruence

• ∠BAC = ∠ EDF

By, CPCT

• ∠A = ∠D

Hence, proved

Answer 2

Answer:

Two circles are said to be congruent if and only if their radii are equal.

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Let AB & CD are two equal chords of two congruent circles with Centre O and O’. i.e AB= CD.

To Prove: ∠AOB = ∠CO'D

Proof:

In ΔAOB and ΔCO'D,

AB = CD ( given)

OA = O'C (Radii of congruent circles)

OB = O'D (Radii of congruent circles)

ΔAOB ≅ ΔCO'D (SSS congruence rule)

∠AOB = ∠CO'D (By CPCT)

Hence, equal chords of congruent circles subtend equal angles at their centres.

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Hope this will help you....