Problem

Source: German TSTST (VAIMO) 2022 P4

Tags: geometry, circumcircle, perpendicular bisector



Let $ABC$ be an acute triangle and let $\omega$ be its circumcircle. Let the tangents to $\omega$ through $B,C$ meet each other at point $P$. Prove that the perpendicular bisector of $AB$ and the parallel to $AB$ through $P$ meet at line $AC$.