This assignment is to explore tangent circles.
We first look at the case were one circle is inside another. There are two types of tangent circles that can be constructed
a. so that the smaller circle is external to the tangent circle. Script
b. so that the smaller circle is internal to the tangent circle. Script
We now look at the loci of the centers of the tangent circles in both of the above cases.
In each case the locus is an ellipse.
The second case to look at is if the two circles intersect.
Using the two cases from above, we get the pictures below
a. tangent circle is internal to one circle and external to the other
b. tangent circle is external to both or internal to both
We once again look at the loci of the centers of the tangent circles.
In the first case, we have an ellipse once again, but in the second case we have a hyperbola.
Last, we look at the case where the two circles are disjoint.
Once again, we get two cases
a. tangent cirle is internal to one circle and external to the other
Finally, we look at the loci of the centers of the tangent circles of these circles.
In bothe of these coses the locus is a hyperbola.