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Perpendicularity in the Incircle Chord Lemma

Source: 2016 KMO Senior #5

November 12, 2016
geometryincentercircumcircle

Problem Statement

A non-isosceles triangle △ABC\triangle ABC has incenter II and the incircle hits BC,CA,ABBC, CA, AB at D,E,FD, E, F. Let EFEF hit the circumcircle of CEICEI at P≠EP \not= E. Prove that △ABC=2△ABP\triangle ABC = 2 \triangle ABP.
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