Question 84
Point $M$ is the midpoint of the side $AB$ of the acute-angled triangle $ABC$, points $P$ and $Q$ are the feet of the altitudes $AP$ and $BQ$. A circle passing through $B, M, P$, touches the side $AC$. Prove that a circle passing through $A, M, Q$ touches the extension of the side $BC$.
(I. Voronovich)
(I. Voronovich)