RU-SPB 2017 Problem 115

Given a tetrahedron $PABC$ , draw the height $PH$ from vertex $P$ to $ABC$ . From point $H$ , draw perpendiculars $HA',HB',HC'$ to the lines $PA,PB,PC$ . Suppose the planes $ABC$ and $A'B'C'$ intersects at line $\ell$ . Let $O$ be the circumcenter of triangle $ABC$ . Prove that $OH\perp \ell$ .