Tangent
Circles

by
Kasey Nored

Given
Circle A and Circle B construct a third Circle C, such that Circle C is tangent
to Circle A and Circle C.

The
tangent circles would look something like this…

This
construction has been completed and the script tool can be viewed here.

To
further explore these circles we will discuss the tangent circles when our two
given circles intersect.

One
can see that 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 find the image below.

One
can see that circle B clearly intersects with Circle A and those intersections
are on the path of the hyperbola created by the trace of the center of circle
C.

This
relationship is maintained regardless of the relative size of Circle A and
Circle B.