RU-SPB 2021 Problem 116

Point $M$ is the midpoint of base $AD$ of an isosceles trapezoid $ABCD$ with circumcircle $\omega$ . The angle bisector of $ABD$ intersects $\omega$ at $K$ . Line $CM$ meets $\omega$ again at $N$ . From point $B$ , tangents $BP, BQ$ are drawn to $(KMN)$ . Prove that $BK, MN, PQ$ are concurrent.

A. Kuznetsov