MathDB

Let

O

and

H

be the circumcenter and orthocenter of a scalene triangle

ABC

, respectively. Let

D

be the intersection point of the lines

AH

and

BC

. Suppose the line

OH

meets the side

BC

X

. Let

P

and

Q

be the second intersection points of the circumcircles of

\triangle BDH

and

\triangle CDH

with the circumcircle of

\triangle ABC

, respectively. Show that the four points

P, D, Q

and

X

lie on a circle.

G4