Question 151
The altitudes of an acute-angled triangle $ABC$ meet at $H$. The points $B_1$ and $C_1$ are chosen on the segments $BH$ and $CH$, respectively, so that $B_1C_1 \parallel BC$. It appeared that the center of the circumcircle $\omega$ of $\triangle B_1HC_1$ lies on the line $BC$. Prove that $\omega$ is tangent to the circumcircle $\Gamma$ of $\triangle ABC$.
(A. Kuznetsov)
(A. Kuznetsov)