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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 ACAC and BDBD of a circle kk meet at the point KK, and let OO be the center of kk. Let MM and NN be the circumcenters of triangles AKBAKB and CKDCKD. Show that the quadrilateral OMKNOMKN is a parallelogram.