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Ratio of areas - triangle:quadrilateral

Source: Canadian Mathematical Olympiad - 1978 - Problem 4.

May 14, 2011

ratiogeometrygeometry proposed

Problem Statement

The sides

AD

and

BC

of a convex quadrilateral

ABCD

are extended to meet at

E

. Let

H

and

G

be the midpoints of

BD

and

AC

, respectively. Find the ratio of the area of the triangle

EHG

to that of the quadrilateral

ABCD