By

SOMIN KIM

First, there are two type of Tangent Circle, when two circles are given.

Case1. the tangent circle goes around, connecting a large circle and connecting external surface of tangent circle with a small circle.

Case2. the tangent circle goes around, connecting a large circle and connecting internal surface of tangent circle with a small circle.

Case 1. ----------------------------------------------------------------- Case 2. --------------------------------------------------------

Each one case can be divided into three cases by the location of two given circles.

There are three cases for case1.

Case1-1: One given circle lies fully inside the other. To view the locus of the center of case1-1 click here.

Case1-2: The 2 given circles intersect one another. To view the locus of the center of case1-2 click here.

Case1-3: The 2 given circles form completely disjoint circular regions. To view the locus of the center of case1-3 click here.

There are three cases for case2.

Case2-1: One given circle lies fully inside the other. To view the locus of the center of case2-1 click here.

Case2-2: The 2 given circles intersect one another. To view the locus of the center of case2-2 click here.

Case2-3: The 2 given circles form completely disjoint circular regions. To view the locus of the center of case2-3 click here.

In these investigations, I realized that all 6 cases either an ellipse or a hyperbola is formed.

The ellipse appears at case1-1, 1-2, and case2-1. The hyperbola appears at case1-3,case2-2, and case2-3.

If you look carefuly, you can find a feature of locus at case 1-1.

You can see sum of the length of CF and FE is fixed no matter where the point F is on the ellipse.