MathDB

Let

ABC

be an acute-angled triangle with circumcircle

\Gamma

and orthocentre

H

. Let

K

be a point of

\Gamma

on the other side of

BC

from

A

. Let

L

be the reflection of

K

in the line

AB

, and let

M

be the reflection of

K

in the line

BC

. Let

E

be the second point of intersection of

\Gamma

with the circumcircle of triangle

BLM

. Show that the lines

KH

EM

and

BC

are concurrent. (The orthocentre of a triangle is the point on all three of its altitudes.)
Luxembourg (Pierre Haas)

Problem Statement