Exradius
Excircle
The radius of an excircle. Let a triangle have exradius (sometimes denoted
), opposite side of length
and angle
, area
, and semiperimeter
. Then
(Johnson 1929, p. 189), where
is the circumradius. Let
be the inradius, then
(4)
(5) (Casey 1888, p. 65) and
(6) Some fascinating formulas due to Feuerbach are
$r_2r_3+r_3r_1+r_1r_2-rr_1-rr_2-rr_3=\frac{1}{2(a^2+b^2+c^2)}