BRC Problem of the Month - November 1999

The first part of this problem isn't too difficult, but the second is much more challenging.  A ruler and compass construction of this figure would also seem to be a challenging problem.

Squeezing circles into tight spaces

Two circles are tangent to the same side of a line at different points, P and Q and are tangent to one another at a third point R.  A third circle lies in the "triangular" region PQR and is tangent to the first two circles and the line.

(a)  If the first two circles both have radius r, what is the radius of the third circle?
(b) More generally, if the radii of the first two circles are and , what is the radius of the third circle.

BRC Problem Index