A quadrilateral ABCD is inscribed into a circle ω with center O. Let M1 and M2 be the midpoints of segments AB and CD respectively. Let Ω be the circumcircle of triangle OM1M2. Let X1 and X2 be the common points of ω and Ω and Y1 and Y2 the second common points of Ω with the circumcircles of triangles CDM1 and ABM2. Prove that X1X2//Y1Y2. geometrycirclescyclic quadrilateral