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.