There are four Circles that touch all the sides of a given Triangle. These are all touched by the Circle through the intersection of the Angle Bisectors of the Triangle, known as the Nine-Point Circle.

Given the above figure, , since

Because , it follows that .

The line tangent to a Circle of Radius centered at

through can be found by solving the equation

giving

Two of these four solutions give tangent lines, as illustrated above.

**References**

Dixon, R. *Mathographics.* New York: Dover, p. 21, 1991.

Honsberger, R. *More Mathematical Morsels.* Washington, DC: Math. Assoc. Amer., pp. 4-5, 1991.

© 1996-9

1999-05-26