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Ratio of triangle areas

Source: Sharygin Geometry Olympiad 2012 - Problem 14

April 28, 2012

ratiogeometrygeometry unsolved

Problem Statement

In a convex quadrilateral

ABCD

suppose

AC \cap BD = O

and

M

is the midpoint of

BC

. Let

MO \cap AD = E

. Prove that

\frac{AE}{ED} = \frac{S_{\triangle ABO}}{S_{\triangle CDO}}