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collinear wanted, given intersections and perpendulars of cyclic ABCD

Source: KJMO 2010 p7

May 3, 2019
collineargeometrycyclic quadrilateralperpendicular

Problem Statement

Let ABCDABCD be a cyclic convex quadrilateral. Let EE be the intersection of lines AB,CDAB,CD. PP is the intersection of line passing BB and perpendicular to ACAC, and line passing CC and perpendicular to BDBD. QQ is the intersection of line passing DD and perpendicular to ACAC, and line passing AA and perpendicular to BDBD. Prove that three points E,P,QE, P,Q are collinear.
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