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

Geometry, Theorems and Problems

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.
 

Tangent Circles, Harmonic Mean, Radius
 

 

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