Problem 288.
Tangent circles, Harmonic Mean, Radius, Diameter

In the figure below, AB is the
diameter of a circle C, circles A (radius R) and B (radius r)
are tangent at D. Circle E is tangent to circles A, B, and C.
Prove that the radius x of circle E is one-fourth the
harmonic mean of R and r.
View or post a solution.