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area chasing, 2 equal ratios in quadrilateral (VII Soros Olympiad R1 9.7)

Source:

July 4, 2021

geometryareas

Problem Statement

Sides

AB

and

CD

of quadrilateral

ABCD

intersect at point

E

. On the diagonals

AC

and

BD

points

M

and

N

are taken, respectively, so that

AM / AC = BN / BD = k

. Find the area of a triangle

EMN

if the area of

ABCD

S