MathDB
Geometry contest 2014 Problem 5

Source:

December 17, 2014
geometrycircumcircletrigonometrypower of a pointradical axisexterior angle

Problem Statement

In a triangle △ABC\triangle ABC with orthocenter HH, let BHBH and CHCH intersect ACAC and ABAB at EE and FF, respectively. If the tangent line to the circumcircle of △ABC\triangle ABC passing through AA intersects BCBC at PP, MM is the midpoint of AHAH, and EFEF intersects BCBC at GG, then prove that PMPM is parallel to GHGH.
Proposed by Sreejato Bhattacharya
Back to ProblemsView on AoPS