 Tangent Circles

Kasey Nored

Given circle A and circle B, construct circle C such that circle C is tangent to circle A and circle B.

The tangent circles would look something like this... The construction for these has been completed and you can view and use the script tool here.

In an attempt at further exploration of these circle we will discuss the tangent circles when our two given circles intersect. As you can see circle B clearly intersects with circle A. If we trace the path of the center of circle C as we animate the point where circle C is tangent to circle A we see the image below. You can watch the trace develop here. One can see that circles A and B intersect and the path of point C is an conic section. The conic section is maintained regardless of the size of A and B. The closer circle A and B get to having the same size the more circular our trace becomes.

For further exploration, one could examine where circles A and B are not intersecting nor is one contained in the other with this GSP file.