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JBMO Shortlist 2013, G4

Source: JBMO Shortlist 2013, G4

June 11, 2017
incentercircumcircleexcirclegeometryperpendicular

Problem Statement

Let II be the incenter and ABAB the shortest side of the triangle ABCABC. The circle centered at II passing through CC intersects the ray ABAB in PP and the ray BABA in QQ. Let DD be the point of tangency of the AA-excircle of the triangle ABCABC with the side BCBC. Let EE be the reflection of CC with respect to the point DD. Prove that PE⊥CQPE\perp CQ.
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