Problem

Source: Iran MO 3rd Round 2024 Geometry Exam P2

Tags: geometry



Let $M$ be the midpoint of the side $BC$ of the $\triangle ABC$. The perpendicular at $A$ to $AM$ meets $(ABC)$ at $K$. The altitudes $BE,CF$ of the triangle $ABC$ meet $AK$ at $P, Q$. Show that the radical axis of the circumcircles of the triangles $PKE, QKF$ is perpendicular to $BC$.