Assignment 7: Tangent Circles

Prepare a retrospective summare on your experience with this assignment. The summary might take a mathematical bent, stressing the underlying theorems and relationships. It might take a pedagogical bent, stressing the exploration and discovery. It might take a "here is something interesting I found" bent. Or... be creative...

Summary of the Assignment

The problem that begins investigation 7 is as follows.

Given two circles and a point on one of the circles. Consturct a circle tangent to the two circles with one point of tangency being the designated point.

I went through the steps and consturcted the tangent circle. My designated point of tangenct is on the larger circle.

The two original circles are labeled c1 and c2. The tangent circle is green and is not labeled. Our next tast was the following problem. Given the construction, however, consider the locus of the center of all such circles tangent to the two given circles. With GSP, we can animate around the circle and trace the locus of the center.

We were asked to construct the tangent circle to two given circles if the given point is on the smaller of the two circles. We should look at the tangent circle when the smaller circle is external to the tangent circle and when the smaller circle is internal the tangent circle.

Now we can look at the locus of the centers. It is not an ellipse but it is an hyperbola.

If we look at the case when the smaller circle is external the tangent circle, we will get similar results.