000RM.dvi

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

.