Let ABCD be a cyclic quadrilateral whose sides have pairwise different lengths. Let O be the circumcenter of ABCD. The internal angle bisectors of ∠ABC and ∠ADC meet AC at B1 and D1, respectively. Let OB be the center of the circle which passes through B and is tangent to AC at D1. Similarly, let OD be the center of the circle which passes through D and is tangent to AC at B1.Assume that BD1∥DB1. Prove that O lies on the line OBOD. geometrycircumcircleprojective geometry