Ford Circles

Stage: 5 Challenge Level: Challenge Level:3 Challenge Level:3 Challenge Level:3

The proof of this striking result is elementary and uses a similar method to the problem Baby Circle.


ford circ;es
Given the radii of the circles and the points of contact with the x-axis you can always find the distances DC in terms of the radii.

The circles will be tangent if and only if the distance AB is equal to the sum of the radii.

The circles will be separate if and only if the distance AB is greater than the sum of the radii.

It is possible to prove that the circles given can never overlap, that is the distance AB is never less than the sum of the radii.

Published November 2009,December 2009.