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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:
 .
"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 Problems
81,
82,
83.
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