MathDB
IMO ShortList 2003, geometry problem 5

Source: German pre-TST 2004, problem 6; Singapore TST 2004; Swiss TST 2004

May 10, 2004
geometryincentercircumcircleIMO ShortlistTriangle

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, Korea