5

Part of 1995 Taiwan National Olympiad

Problems(1)

Source: 4-th Taiwanese Mathematical Olympiad 1995

P

be a point on the circumcircle of a triangle

A_{1}A_{2}A_{3}

H

be the orthocenter of the triangle. The feet

B_{1},B_{2},B_{3}

of the perpendiculars from

P

A_{2}A_{3},A_{3}A_{1},A_{1}A_{2}

lie on a line. Prove that this line bisects the segment

PH

geometrycircumcirclegeometry unsolved