MathDB

In an acute-angled triangle

ABC

, the point

H{}

is the orthocenter,

M{}

is the midpoint of the side

BC

and

\omega

is the circumcircle. The lines

AH, BH

and

CH{}

intersect

\omega

a second time at points

D, E

and

F{}

respectively. The ray

MH

intersects

\omega

at point

J{}

. The points

K{}

and

L{}

are the centers of the inscribed circles of the triangles

DEJ

and

DFJ

respectively. Prove that

KL\parallel BC

Problem Statement