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In the figure below, given a
triangle AED, M and N are the midpoints of cevians AC and DB
respectively. If S1 and S2 are the areas of the quadrilaterals
AECN and DEBM respectively, prove that:
 .
"A great discovery solves a great problem, but there is a grain
of discovery in the solution of any problem. Your problem may be
modest, but if it challenges your curiosity and brings into play
your inventive faculties, and if you solve it by your own means,
you may experience the tension and enjoy the triumph of
discovery. Such expert experiences at a susceptible age may
create a taste for mental work and leave their imprint on mind
and character for a lifetime." George Polya, 1944
HINTS:
1. CEVIAN:
A Cevian is a line segment which
joins a vertex of a triangle with a point on the opposite side
(or its extension).
2. See Proposed Problem
87
3. AREA OF A TRIANGLE:
Median Area Fact:
A median divides the triangle into
two triangles of equal area.
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