Assignment 7: Tangent Circles

By Kendyl Wade

For this assignment, we will explore tangent circles and the traces of the centers of the tangent circles.

How to construct a tangent circle:

1)

2) 3) 4) 5) 6)7)

If we start with two circles (C1 and C2), there are three different cases:

1) C1 is within C2.

2) C1 intersects C2.

3) C1 is outside, and does not intersect, C2.

CASE 1: C1 is within C2 (or vise versa)

Here is a GSP file that shows the trace of the center of this tangent circle.

It appears that the trace of the center of the tangent circle creates an ellipse, and that the centers of C1 and C2 are the foci.

Case 2: C1 intersects C2

Here is a GSP file that shows the trace of the center of this tangent circle.

Case 3: C1 is outside, and does not intersect, C2

Here is a GSP file that shows the trace of the center of this tangent circle.

The trace of the center of the tangent circle appears to create a hyperbola with the foci being the centers of C1 and C2.