Assignment 7

by

Allison McNeece

For this assignment we will be looking at tangent circles (a.k.a. "kissing circles")

Given any two circles find the circle that is tangent two both of these circles with one point of tangency being the designated point.

Below is an example for you to play with. The given circles are green and the tangent circle is blue. The designated point of tangency is blue and labeled A.

#### Sorry, this page requires a Java-compatible web browser.Move A around to explore how the tangent circle changes. Increase and decrease the sizes of the green circles. How does this impact the tangent circle?

There are actually two different tangent circles that can be constructed using A as the designated tangency point.

Below the orange circle is the tangent circle.

#### Sorry, this page requires a Java-compatible web browser.How does this tangent circle differ from the first one?

Let us now explore the loci of the centers of the these tangent circles. We will examine the following cases for both forms of tangent circles:

 1. one circle is inside the other 2. the circles intersect 3. the circles are disjoint

Case 1: One circle is inside the other

#### Sorry, this page requires a Java-compatible web browser.The locus of the orange tangent circle

Case 2: The circles intersect

#### Sorry, this page requires a Java-compatible web browser.The locus of the orange circle

Case 3: The circles are disjoint