MathDB

In a triangle

ABC

, let

P

be a point on its circumscribed circle (on the arc

AC

that does not contain

B

). Let

H,H_1,H_2

and

H_3

be the orthocenters of triangles

ABC, BCP, ACP

and

ABP

, respectively. Let

L = PB \cap AC

and

J = HH_2 \cap H_1H_3

. If

M

and

N

are the midpoints of

JH

and

LP

, respectively, prove that

MN

and

JL

intersect at their midpoint.

Problem Statement