This is a Sangaku problem, featured on p. 70 of Paul Lockhart's book Measurement. [br][url=http://www.youtube.com/watch?v=V1gT2f3Fe44&t=1m35s]See Lockhart introduce it[/url].[br][*]Two circles lie on a line, touching each other at a point. A small circle is inscribed in the space between. How does its radius depend on the radii of the two larger circles?[br][br][color=#00FF00]Point A[/color] is free; [color=#FFFF00]Point B[/color] remains tangent to the ground and the circle defined by point A; [color=#FF0000]Points [math]C_1[/math]and [math]C_2[/math][/color] are dependent on [color=#00FF00]A[/color] and [color=#FFFF00]B[/color].

[url=http://www.youtube.com/watch?v=V1gT2f3Fe44&t=1m35s]See Lockhart's video[/url]