Question

Prove that two equal chords of a circle subtend equal angles at the centre of the circle​

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. Thus, ∠AOB = ∠COD by CPCT. Equal chords of congruent circles subtend equal angles at their centres.

Answer 2

Step-by-step explanation:

In ΔAOB and ΔCOD,

AB=CD (Given)

AO=CO (radius)

OB=OD (radius)

By S.S.S congruency, ΔAOB≅ΔCOD

⇒∠AOB=∠COD.

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