A triangle surrounded by circles

Geometry Level 5

In a circle AA with radius 18+4326\frac{18+\sqrt{432}}{6} we draw 33 circles with equal radii, in such way that each of them are tangent to the other 22 circles and to circle AA. Inside the circle AA we draw a circle BB in such way that is tangent to each of the 33 new circles. An equilateral triangle CC is inscribed in BB.

If the area of CC can be written in the form:

abcd\dfrac{a\sqrt{b}-c}{d}

Where a,b,ca,b,c and dd are integers such that bab|a and dcd|c.

Find:

a+b+c+da+b+c+d

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