MathDB

Quadrilateral

ABCD

is given with

AD \nparallel BC

. The midpoints of

AD

and

BC

are denoted by

M

and

N

, respectively. The line

MN

intersects the diagonals

AC

and

BD

in points

K

and

L

, respectively. Prove that the circumcircles of the triangles

AKM

and

BNL

have common point on the line

AB

.( Proposed by Emil Stoyanov ) http://estoyanov.net/wp-content/uploads/2015/09/est.png

Problem Statement