In the figure below, given a triangle
ABC, S_{1} is the area of contact triangle of the
incircle, S_{a}, S_{b}, and S_{c} are
the areas of the contact triangles of the excircles. Prove that:
\(\dfrac{1}{S_1}=\dfrac{1}{S_a}+\dfrac{1}{S_b}+\dfrac{1}{S_c}\).
.
**
HINTS: **
**1. See Problems
82,
83,
84.** |