MathDB

Parallel lines and midpoints

Source: Ukrainian National Math Olympiad 4th round

October 20, 2014

geometryparallelogramgeometry unsolved

Problem Statement

Let

M

be the midpoint of the side

BC

\triangle ABC

. On the side

AB

and

AC

the points

E

and

F

are chosen. Let

K

be the point of the intersection of

BF

and

CE

and

L

be chosen in a way that

CL\parallel AB

and

BL\parallel CE

. Let

N

be the point of intersection of

AM

and

CL

. Show that

KN

is parallel to

FL

. Edit:Fixed typographical error.