TW-TST 1995 Problem 5

Let $P$ be a point on the circumcircle of a triangle $A_{1}A_{2}A_{3}$ , and let $H$ be the orthocenter of the triangle. The feet $B_{1},B_{2},B_{3}$ of the perpendiculars from $P$ to $A_{2}A_{3},A_{3}A_{1},A_{1}A_{2}$ lie on a line. Prove that this line bisects the segment $PH$ .