236 The classical triangle centers
8.5 The excenters and the excircles
The internal bisector of each angle and theexternalbisectors of the re-
maining two angles are concurrent at anexcenterof the triangle. An
excirclecan be constructed with this as center, tangent to the lines con-
taining the three sides of the triangle.
Z
X
Y
Ic
Ib
Ia
C
A
B
The exradii of a triangle with sidesa,b,care given by
ra=
s−a
,rb=
s−b
,rc=
s−c