MathDB

Let

\omega

and

O

be respectively the circumcircle and the circumcenter of a triangle

ABC

. The line

AO

intersects

\omega

second time at

A'

M_B

and

M_C

are the midpoints of

AC

and

AB

, respectively. The lines

A'M_B

and

A'M_C

intersect

\omega

secondly at points

B'

and

C

, and also intersect

BC

at points

D_B

and

D_C

, respectively. The circumcircles of

CD_BB'

and

BD_CC'

intersect at points

P

and

Q

. Prove that

O

P

Q

are collinear.
(М. Германсков)
Thanks to the user Vlados021 for translating the problem.

Problem Statement