Some Interesting Sets of Circles

Extract

The “curious” property noted by Mr. A. P. Rollett (Note 1261 in the Mathematical Gazette for December 1937), with regard to the centres of circles touching one another and inscribed in the space between two given circles, leads to an interesting general theorem on all such sets of circles.

Given any two circles, and a set of circles touching one another and the two given circles, then, if r₁r₂, r₃ are the radii of three successive circles of the set, of which r₂ is known, r₁ and r₃ are the roots of a quadratic equation of which the coefficients are simple functions of r₂ and the radii of the given circles.