Take three unit circles, each touching the other two. Construct three circles C1, C2 and C3, with radii r1, r2 and r3, respectively, as in the figure below. The circles that are tangent to all three unit circles are C1 and C3, with C1 the smaller of these. The circle through the three points of tangency of the unit circles is C2. Find the radii r1, r2 and r3, and show that r1r3=r22.