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Given a triangle ABC of area S, the excircle of center
D,
the exradius ra,
and the circumradius R. If Sa is the area of the
contact triangle EFG, from the tangent points of the excircle
and triangle ABC, prove
that:
Post your solutions or ideas in the
blog.
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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
80,
81,
82.
2. AREA OF A TRIANGLE:
Semiperimeter and Exradius Formula
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