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ISL 2003 G5 page doesnot exist on AoPS?

Source: ISL 2003 G5

October 25, 2019
geometryIMO Shortlist

Problem Statement

Let ABCABC be an isosceles triangle with AC=BCAC=BC, whose incentre is II. Let PP be a point on the circumcircle of the triangle AIBAIB lying inside the triangle ABCABC. The lines through PP parallel to CACA and CBCB meet ABAB at DD and EE, respectively. The line through PP parallel to ABAB meets CACA and CBCB at FF and GG, respectively. Prove that the lines DFDF and EGEG intersect on the circumcircle of the triangle ABCABC.
Proposed by Hojoo Lee
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