Three circles of radius 6, 7, and 8 are externally tangent to each other. There exists a smaller circle tangent to all three (in the space created between the three original circles).

What is the radius of this smallest circle?

If you want to construct the two Soddy circles. First invert through a circle with one of the points of tangency as a center and passing through one of the others. Construction of the inverted Soddy circles is then simple. Inverting these inverted circles gives the Soddy circles.

Posted by Bractals on 2004-07-29 10:16:04