MathDB

A triangle

ABC

is given. Let

M

be the midpoint of the side

AC

of the triangle and

Z

the image of point

B

along the line

BM

. The circle with center

M

and radius

MB

intersects the lines

BA

and

BC

at the points

E

and

G

respectively. Let

H

be the point of intersection of

EG

with the line

AC

, and

K

the point of intersection of

HZ

with the line

EB

. The perpendicular from point

K

to the line

BH

intersects the lines

BZ

and

BH

at the points

L

and

N

, respectively. If

P

is the second point of intersection of the circumscribed circles of the triangles

KZL

and

BLN

, prove that, the lines

BZ, KN

and

HP

intersect at a common point.

Problem Statement