MathDB

concurrency in a parallelogram (Kyiv City Olympiad 2006 9.4)

Source:

June 28, 2020

geometryparallelogramconcurrencyconcurrent

Problem Statement

On the sides

AB

and

CD

of the parallelogram

ABCD

mark points

E

and

F

, respectively. On the diagonals

AC

and

BD

chose the points

M

and

N

so that

EM\parallel BD

and

FN\parallel AC

. Prove that the lines

AF, DE

and

MN

intersect at one point.
(B. Rublev)