ABCD is convex quadrilateral with AB=CD. AC and BD intersect in O. X,Y,Z,T are midpoints of BC,AD,AC,BD. Prove, that circumcenter of OZT lies on XY.
Source: St Petersburg Olympiad 2009, Grade 10, P2
Tags: geometry, circumcircle
ABCD is convex quadrilateral with AB=CD. AC and BD intersect in O. X,Y,Z,T are midpoints of BC,AD,AC,BD. Prove, that circumcenter of OZT lies on XY.