Equal distances between pairs of orthocenters in cyclic quad
Source: XVII Tuymaada Mathematical Olympiad (2010), Senior Level
July 31, 2011
geometrycircumcirclegeometric transformationreflectioncyclic quadrilateralgeometry unsolved
Problem Statement
In a cyclic quadrilateral , the extensions of sides and meet at point , and the extensions of sides and meet at point . Prove that the distance between the orthocenters of triangles and is equal to the distance between the orthocenters of triangles and .