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Quadrilateral ABCD such that AC+AD=BC+BD

Source: Canadian MO 2012 #3

May 4, 2012
geometrycalculusincenterconicsellipseangle bisectorgeometry proposed

Problem Statement

Let ABCDABCD be a convex quadrilateral and let PP be the point of intersection of ACAC and BDBD. Suppose that AC+AD=BC+BDAC+AD=BC+BD. Prove that the internal angle bisectors of ∠ACB\angle ACB, ∠ADB\angle ADB and ∠APB\angle APB meet at a common point.
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