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upgrade of problem 7 for grade 8-9, 239MO 2004

Source: 239MO 2004, grade 10-11, problem 8

December 11, 2004
geometrycircumcircleparallelogramconicsparabolaratiogeometric transformation

Problem Statement

Given a triangle ABCABC. A point XX is chosen on a side ACAC. Some circle passes through XX, touches the side ACAC and intersects the circumcircle of triangle ABCABC in points MM and NN such that the segment MNMN bisects BXBX and intersects sides ABAB and BCBC in points PP and QQ. Prove that the circumcircle of triangle PBQPBQ passes through a fixed point different from BB. proposed by Sergej Berlov
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