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Problem 84. Contact Triangles
Areas, Incircle, Excircle.
Level: High School, SAT Prep, College
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In the figure below, given a triangle ABC, the
incircle of radius r and the contact triangle of area S1,
the excircle of radius ra and the contact triangle of
area Sa. 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
82.
2. See Proposed Problems
83.
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