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In the figure above, ABCD is a
trapezoid of area S with AD parallel to BC and E the point of intersection of the diagonals AC and BD. If S1,
S2,
S3, and S4
are the areas of triangles BEC, AED, ABE, and CED respectively,
(1) prove that
 ,
and (2) prove that
 .
See also: Problem
163.
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