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collinear wanted, AE = NE, CE = ME, rhombus related

Source: Oral Moscow Team MO 2017 IX p5 / All-Russian MO 1993 Regional (Round 4) 9.7

September 19, 2020

geometryrhombuscollinearequal segments

Problem Statement

On the diagonal

AC

of the rhombus

ABCD

, a point

E

is taken, which is different from points

A

and

C

, and on the lines

AB

and

BC

are points

N

and

M

, respectively, with

AE = NE

and

CE = ME

. Let

K

be the intersection point of lines

AM

and

CN

. Prove that points

K, E

and

D

are collinear.