Given : A circle with center O and two angles formed at center.
∠AOB = ∠COD ……(i)
To Prove : \(\widehat { AB }\) = \(\widehat { CD }\)
Construction : Join OA, OB, OC and OD by center O.
Proof : In ∆AOB and ∆COD (given)
AO = OD (radius of circle)
OB = OC (radius of circle)
∠AOB = ∠COD (given)
By SAS congruence criterion
∆AOB = ∆COD
Thus, By CPCT
AB = CD
Chord AB = Chord CD and AB = CD
