MathDB
Hard geometry

Source: Serbia 2008

April 13, 2008
geometrycircumcirclegeometric transformationhomothetysimilar trianglesgeometry unsolved

Problem Statement

Triangle △ABC \triangle ABC is given. Points D D i E E are on line AB AB such that D \minus{} A \minus{} B \minus{} E, AD \equal{} AC and BE \equal{} BC. Bisector of internal angles at A A and B B intersect BC,AC BC,AC at P P and Q Q, and circumcircle of ABC ABC at M M and N N. Line which connects A A with center of circumcircle of BME BME and line which connects B B and center of circumcircle of AND AND intersect at X X. Prove that CX⊥PQ CX \perp PQ.
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