MathDB

Let

B

and

C

be arbitrary points on sides

AP

and

PD

respectively of an acute triangle

APD

. The diagonals of the quadrilateral

ABCD

meet at

Q

, and

H_1,H_2

are the orthocenters of triangles

APD

and

BPC

, respectively. Prove that if the line

H_1H_2

passes through the intersection point

X \ (X \neq Q)

of the circumcircles of triangles

ABQ

and

CDQ

, then it also passes through the intersection point

Y \ (Y \neq Q)

of the circumcircles of triangles

BCQ

and

ADQ.

Problem Statement