Power of three!

Geometry Level 4

Three circles \(C_1, C_2, C_3\) of radii \(a , b, c\), respectively, touch each other externally at three different points, as shown in the figure above.

If their points of contact are all 4 units away from the radical center \(O\) of the three circles, then evaluate \[ \dfrac{abc}{a+b+c}.\]

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