MathDB
PBQ passes through the circumcentre of triangle ABC

Source: 239MO 2004, grade 8-9, problem 7

December 11, 2004
geometrycircumcircleparallelogramsymmetryperpendicular bisectorgeometry solved

Problem Statement

Given an isosceles triangle ABCABC (with AB=BCAB=BC). 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 the circumcentre of triangle ABCABC. proposed by Sergej Berlov
Back to ProblemsView on AoPS