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.