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4 concyclic points

Source: Japan Mathematical Olympiad Finals 2015 Q4

April 1, 2016
geometrycircumcircleincenter

Problem Statement

Scalene triangle ABCABC has circumcircle Γ\Gamma and incenter II. The incircle of triangle ABCABC touches side AB,ACAB,AC at D,ED,E respectively. Circumcircle of triangle BEIBEI intersects Γ\Gamma again at PP distinct from BB, circumcircle of triangle CDICDI intersects Γ\Gamma again at QQ distinct from CC. Prove that the 44 points D,E,P,QD,E,P,Q are concyclic.
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