MathDB

Let

ABC

be a scalene triangle, and points

O

and

H

be its circumcenter and orthocenter, respectively. Point

P

lies inside triangle

AHO

and satisfies

\angle AHP = \angle POA

. Let

M

be the midpoint of segment

\overline{OP}

. Suppose that

BM

and

CM

intersect with the circumcircle of triangle

ABC

again at

X

and

Y

, respectively.
Prove that line

XY

passes through the circumcenter of triangle

APO

.
Proposed by Li4

Problem Statement