MathNet 2009-part-03 — 175 problems (EN–VI) Question 142

In an acute triangle $ABC$, the altitudes $AA_1$, $BB_1$, $CC_1$ are drawn. A perpendicular to $AC$ passing through $A_1$ intersects line $B_1C_1$ at $D$. Prove that $\angle ADC = 90^\circ$.