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Circumcentre, Incentre, Intersection of Diagonals Collinear

Source: Czech-Polish-Slovak 2005 Q2

April 27, 2013
geometryincentersearchgeometry unsolved

Problem Statement

A convex quadrilateral ABCDABCD is inscribed in a circle with center OO and circumscribed to a circle with center II. Its diagonals meet at PP. Prove that points O,IO, I and PP lie on a line.
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