The Inscribed Circle of a Triangle . The center is called the Incenter and the Radius the Inradius. The points of intersection of the incircle with are the Vertices of the Pedal Triangle of with the Incenter as the Pedal Point (c.f. Tangential Triangle). This Triangle is called the Contact Triangle.

The Area of the Triangle is given by

where is the Semiperimeter.

Using the incircle of a Triangle as the Inversion Center, the sides of the Triangle and its Circumcircle are carried into four equal Circles (Honsberger 1976, p. 21). Pedoe (1995, p. xiv) gives a Geometric Construction for the incircle.

**References**

Coxeter, H. S. M. and Greitzer, S. L. *Geometry Revisited.* Washington, DC: Math. Assoc. Amer., pp. 11-13,
1967.

Honsberger, R. *Mathematical Gems II.* Washington, DC: Math. Assoc. Amer., 1976.

Johnson, R. A. *Modern Geometry: An Elementary Treatise on the Geometry of the Triangle and the Circle.*
Boston, MA: Houghton Mifflin, pp. 182-194, 1929.

Pedoe, D. *Circles: A Mathematical View, rev. ed.* Washington, DC: Math. Assoc. Amer., 1995.

© 1996-9

1999-05-26