**EMAT
6700**

**by
Brad Simmons**

**Tangent Circles**

Use geometer's sketchpad investigate tangent circles.

Two circles in the same plane are **tangent circles** is
they have exactly one point in common.

Tangent circles with no common interior point are **externally
tangent**.

If
tangent circles have common interior points, then they are** internally tangent**.

Three
or more circles are **mutually tangent** if each pair of them are tangent.

For more information about Tangent Circles please click here.

1. Make sketches to show all possible positions of three mutually tangent circles.

2. Make sketches to show all possible positions of four mutually tangent circles.

3. Make sketches to show all possible positions of five mutually tangent circles.

4. Write a conjecture about the number of possible
positions for **n** mutually tangent circles if **n** is a whole number
greater than 4.