6 Tangent Circles - special case

Geometry Level pending

A circle of radius 12 12 is laid on the horizontal x y xy plane. Five circles each of radius 16 16 are positioned around it, such that each is tangent to the horizontal circle and to the two neighboring circles, as illustrated in the attached figure. How high above the x y xy plane is the tangency point between two neighboring big circles (points A, B, C, D, E).

The answer is 3.3696.

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