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Collinear points with orthocenters

Source: Korea National Olympiad 2010 Problem 6

September 9, 2012
geometrygeometric transformationhomothetycircumcircleratioprojective geometrygeometry proposed

Problem Statement

Let ABCD ABCD be a cyclic convex quadrilateral. Let E E be the intersection of lines AB,CD AB, CD . P P is the intersection of line passing B B and perpendicular to AC AC , and line passing C C and perpendicular to BD BD. Q Q is the intersection of line passing D D and perpendicular to AC AC , and line passing A A and perpendicular to BD BD . Prove that three points E,P,Q E, P, Q are collinear.
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