Question

28. Prove that equal chords of a circle subtend equal angles at the center​

Answer 1

Answer:

A circle is a collection of points whose every every point is equidistant from the centre. Thus, two circles can only be congruent when they the distance of every point of the both circle is equal from the centre.

Given,

AB = CD (Equal chords)

To prove,

∠AOB = ∠COD

Proof,

In ΔAOB and ΔCOD,

OA = OC (Radii)

OB = OD (Radii)

AB = CD (Given)

∴ ΔAOB ≅ ΔCOD (SSS congruence condition)

Thus, ∠AOB = ∠COD by CPCT.

•Equal chords of congruent circles subtend equal angles at their centres.

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