MathDB
Collinearity in cyclic quadrilateral

Source:

December 2, 2006
geometrycircumcirclesymmetrypower of a pointradical axisgeometry unsolved

Problem Statement

A convex quadrilateral ABCDABCD with AC≠BDAC \neq BD is inscribed in a circle with center OO. Let EE be the intersection of diagonals ACAC and BDBD. If PP is a point inside ABCDABCD such that ∠PAB+∠PCB=∠PBC+∠PDC=90∘\angle PAB+\angle PCB=\angle PBC+\angle PDC=90^\circ, prove that OO, PP and EE are collinear.
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