Let $AA_1$ be an altitude in $\Delta ABC$. Let $H_a$ be the orthocenter of the triangle with vertices the tangential points of the excircle to $\Delta ABC$, opposite to $A$. The points $B_1$, $C_1$, $H_b$, and $H_c$ are defined analogously. Prove that $A_1 H_a$, $B_1 H_b$, and $C_1 H_c$ are concurrent.