MathDB
Favorite line IO

Source: 2024 Turkey TST P1

March 18, 2024
geometryincentercircumcircle

Problem Statement

In triangle ABCABC, the incenter is II and the circumcenter is OO. Let AIAI intersects (ABC)(ABC) second time at PP . The line passes through II and perpendicular to AIAI intersects BCBC at XX. The feet of the perpendicular from XX to IOIO is YY. Prove that A,P,X,YA,P,X,Y cyclic.
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