MathDB
Geometry

Source: Pan African Mathematics Olympiad P2

August 15, 2024
geometryPAMO 2024

Problem Statement

In triangle ABCABC,let MM be the midpoint of the side BCBC,and NN is the midpoint of the segment AMAM,the circle going through NN and tangent the line ACAC at AA intersects the segment ABAB again in PP.
prove that the circumcircle of triangle BPMBPM is tangent the line AMAM