Power of three!

Geometry Level 4

Three circles C1,C2,C3C_1, C_2, C_3 of radii a,b,ca , 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 OO of the three circles, then evaluate abca+b+c. \dfrac{abc}{a+b+c}.

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