MathDB

Let

ABC

be a triangle and

O

be its circumcenter. Let

D

E

and

F

be the respective tangent points of the incircle of

\triangle ABC

, and sides

BC

CA

and

AB

. Let

M

and

N

be the respective midpoints of sides

AB

and

AC

. Let

M'

and

N'

be the respective reflections of points

M

and

N

across lines

DE

and

DF

. Let lines

CM'

and

BN'

intersect lines

DE

and

DF

at points

H

and

J

, respectively. Prove that the points

H

J

and

O

are collinear.
Proposed by Luu Dong, Vietnam

Problem Statement