MathNet 2015-part-04 — 191 problems (EN–VI) Question 65

Let $AH_A, BH_B, CH_C$ be the heights in $\triangle ABC$. We draw perpendiculars $p_A, p_B, p_C$ through the vertices $A, B, C$ to $H_B H_C, H_C H_A, H_A H_B$, respectively. Prove that $p_A, p_B, p_C$ pass through the same point.