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: \(\dfrac{S_a}{S}=\dfrac{r_a}{2\cdot R}\).
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
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