Given a triangle ABC of area S, the
excircle of center D, the exradius r_{a}, and the
circumradius R. If S_{a} is the area of the contact
triangle EFG, from the tangent points of the excircle and
triangle ABC, prove that: \(\dfrac{S_a}{S}=\dfrac{r_a}{2\cdot R}\).
HINTS:
1. See Problems
80,
81,
82.
CONTACT TRIANGLE:
The contact triangle of a triangle
ABC (figure above), also called the intouch triangle, is the
triangle DEF formed by the points of tangency of the incircle of
triangle ABC with triangle ABC.
AREA OF A TRIANGLE:
Semiperimeter and Exradius
Formula
