The locus of the centers of the tangent circles are most interesting in this exercise. Here is a summary of some of my findings after doing the constructions:

The locus of the centers of the tangent circles ...

1. Is an ellipse when the given point is on the perimeter of the large circle and the small circle is exterior to the tangent circle.

2. Is an ellipse when the given point is on the perimeter of the large circle and the small circle is interior to the tangent circle.

3. Is an ellipse when the given point is on the perimeter of the small circle and the small circle is exterior to the tangent circle.

4. Is an ellipse when the given point is on the perimeter of the small circle and the small circle is interior to the tangent circle.

5. Is an ellipse when two circles intersect, the given point is on the larger circle and the smaller circle is exterior to the tangent circle.

6. Is an ellipse when two circles intersect, the given point is on the smaller circle and the smaller circle is exterior to the tangent circle.

7. Is a hyperbola when two circles intersect, the given point is on the smaller circle and the smaller circle is interior to the tangent circle.

8. Is a hyperbola when two circles do not intersect and a tangent circle is drawn between the two given circles.

Back to my Main Page

Back to the First Tangent Circle Page

Back to the Second Tangent Circle Page