Parallelogram
Source: All-Russian 2011
May 17, 2011
geometryparallelogramcircumcirclegeometric transformationreflectionsymmetrygeometry proposed
Problem Statement
On side of parallelogram ( is acute) lies point so that triangle is an acute triangle. Let , , and be the circumcenters of triangles , , and respectively. Prove that the orthocenter of triangle lies on line .