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Convex quadrilateral

Source: 2002 Austrian-Polish, problem 6

September 23, 2006
geometrycircumcirclegeometry unsolved

Problem Statement

The diagonals of a convex quadrilateral ABCDABCD intersect in the point EE. Let UU be the circumcenter of the triangle ABEABE and HH be its orthocenter. Similarly, let VV be the circumcenter of the triangle CDECDE and KK be its orthocenter. Prove that EE lies on the line UKUK if and only if it lies on the line VHVH.
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