1989 APMO Problems/Problem 3
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Problem
Let ,
,
be three points in the plane, and for convenience, let
,
. For
,
, and
, suppose that
is the midpoint of
, and suppose that
is the midpoint of
. Suppose that
and
meet at
, and that
and
meet at
.
Calculate the ratio of the area of triangle
to the area of triangle
.