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 be an isosceles triangle with , whose incentre is . Let be a point on the circumcircle of the triangle lying inside the triangle . The lines through parallel to and meet at and , respectively. The line through parallel to meets and at and , respectively. Prove that the lines and intersect on the circumcircle of the triangle .Proposed by Hojoo Lee, Korea