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In the figure below, given a triangle ABC,
S1 is the area of contact triangle of the incircle, Sa,
Sb, and Sc are the areas of the contact
triangles of the excircles. Prove
that:
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"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. See Proposed Problems
84.
2. TRIANGLE:
Inradius and
Exradii Formula
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