MathDB

Let

O

and

H

be the circumcenter and the orthocenter, respectively, of an acute triangle

ABC

. Points

D

and

E

are chosen from sides

AB

and

AC

, respectively, such that

A

D

O

E

are concyclic. Let

P

be a point on the circumcircle of triangle

ABC

. The line passing

P

and parallel to

OD

intersects

AB

at point

X

, while the line passing

P

and parallel to

OE

intersects

AC

Y

. Suppose that the perpendicular bisector of

\overline{HP}

does not coincide with

XY

, but intersect

XY

Q

, and that points

A

Q

lies on the different sides of

DE

. Prove that

\angle EQD = \angle BAC

.
Proposed by Shuang-Yen Lee

Problem Statement