Three Touching Circles on a Line

The radius

r

1

of the blue circle is 2.

The radius

r

2

of the green circle is 0.5.

The radius

r

3

of the purple circle is

r

1

r

2



r

1

+

r

2



= 0.222222.

The radius of the middle circle (purple) of three circles all touching each other and a line is given by a formula in terms of the radii of the two outside circles. Drag the points to vary the outside circles.