Editing Incircle and excircles (section)

====Radius====
The inradius <math>r</math> of the incircle in a triangle with sides of length <math>a</math>, <math>b</math>, <math>c</math> is given by<ref>{{harvtxt|Kay|1969|p=201}}</ref>
:<math display=block>r = \sqrt{\frac{(s-a)(s-b)(s-c)}{s}},</math>

where <math>s = \tfrac12(a + b + c)</math> is the semiperimeter (see [[Heron's formula]]).

The tangency points of the incircle divide the sides into segments of lengths <math>s-a</math> from <math>A</math>, <math>s-b</math> from <math>B</math>, and <math>s-c</math> from <math>C</math> (see [[Tangent_lines_to_circles#Tangent_lines_to_one_circle|Tangent lines to a circle]]).<ref>Chu, Thomas, ''The Pentagon'', Spring 2005, p. 45, problem 584.</ref>