Two tangent circles are shown below. One circle is centered at (2,4) with radius 4, and the other circle is centered at (6,1) with radius 1. The equation of a common external tangent to the circles can be written in the form y = mx + b with m < 0.

A third circle is drawn which is tangent to both circles. What is the radius of this third circle?

Guest Apr 20, 2022