Question 173
Let $AM$ be a median in an acute triangle $ABC$. Its extension intersect the circumcircle $w$ of $ABC$ at $P$. Let $AH_1$ be an altitude of $\triangle ABC$, $H$ - its orthocenter. The rays $MH$ and $PH_1$ intersect $w$ at $K$ and $T$ respectively. Prove that the circumcircle of $\triangle KTH_1$ is tangent to $BC$.
(Khilko Danylo)
(Khilko Danylo)