The Seven Circles Theorem

This remarkable theorem is quite young. Evelyn, Money-Coutts, and Tyrrell first published it in 1974. The reason for this late discovery could be the difficulty of constructing a circle tangent to three other circles (Apollonius's problem). No practicable way has been found using straightedge and compass.

Mathematica readily solves three simultaneous quadratic equations to determine the tangent circle.

The conclusion also holds when the six circles are tangent to the unit circle from the outside.