Exradius

Excircle

The radius of an excircle. Let a triangle have exradius (sometimes denoted ), opposite side of length and angle , area , and semiperimeter . Then

$r_1	=	\frac{\Delta}{s-a}	

= \sqrt{\frac{s(s-b)(s-c)}{s-a}} = 4R\sin{\frac{A}{2}\cos{\frac{B}{2}}\cos{\frac{C}{2}}$ (Error compiling LaTeX. Unknown error_msg) (Johnson 1929, p. 189), where is the circumradius. Let be the inradius, then

and

(Casey 1888, p. 65) and

Some fascinating formulas due to Feuerbach are

Reference:

Weisstein, Eric W. "Exradius." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Exradius.html