Theorem 10.1 : Equal chords of a circle subtend equal angles at the center Class 9

Theorem 10.1 : Equal chords of a circle subtend equal angles at the center.

Given : a circle with center O. AB is a chord of circle and OM bisects AB.

To prove : ∠AOB = ∠DOC

Proof : In △AOB and △COD 

OA = OD (Radius)

OB = OC (Radius)

AB = CD (Given)

⇒△AOB ⩭ △COD (by SSS congruency)

∠AOB = ∠DOC ( By C.P.C.T. )

Hence proved.

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