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P is the intersection of external bisectors

Source: ItaMO 2011, P4

February 14, 2012
conicsellipsegeometryItaly

Problem Statement

ABCDABCD is a convex quadrilateral. PP is the intersection of external bisectors of ∠DAC\angle DAC and ∠DBC\angle DBC. Prove that ∠APD=∠BPC\angle APD = \angle BPC if and only if AD+AC=BC+BDAD+AC=BC+BD
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