Case Two:

The circles intersect.

In this case, there are still two tangent circles.

Let's look at the locus of the centers of the tangent circles as the point of tangency moves along the larger circle.

Notice that in this case, the locus is NOT two elipses, but one elipse and one hyperbola, yet still the foci are the centers of the original cirrcles.

Click **here**
to open the GSP sketch to see the animation of the tangent circle's
centers.

It is also interesting to look at the envelope of lines formed by tracing the tangent lines.

It is much easier to see the hyperbola in this animation.

Click **here**
to open the GSP sketch.

Click **here**
to return to the Tangent Circles page.

Click **here**
to proceed to CASE THREE.

Click **here**
to return to Julie's main page.