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.