OMKN is a parallelogram (easy geometry)
Source: German TST 2004, exam VII, problem 2, by Arthur Engel; part of AMM problem #10874
June 1, 2004
geometryparallelogramcircumcirclegeometric transformationreflectionperpendicular bisectorgeometry proposed
Problem Statement
Let two chords and of a circle meet at the point , and let be the center of . Let and be the circumcenters of triangles and . Show that the quadrilateral is a parallelogram.