Question 59
$AH_a$, $BH_b$ and $CH_c$ are the altitudes of the triangle $ABC$. Prove that if $\frac{H_b C}{AC} = \frac{H_c A}{AB}$, then the line, symmetric to the line $BC$ with respect to the line $H_b H_c$, is tangent to the circumscribed circle of $\triangle H_b H_c A$.