000RM.dvi

234 The classical triangle centers

8.3 The incenter and the incircle

The internal angle bisectors of a triangle are concurrent at theincenter
of the triangle. This is the center of theincircle, the circle tangent to the
three sides of the triangle.
If the incircle touches the sidesBC,CAandABrespectively atX,
Y, andZ,

AY=AZ=s−a, BX=BZ=s−b, CX=CY=s−c.

s−b

s−b

s−c

s−c

s−a

s−a

Z

X

Y

I

C

A

B

Denote byrthe inradius of the triangleABC.

r=

2

a+b+c

=

s

.