# A triangle surrounded by circles

Geometry Level 4

In a circle $$A$$ with radius $$\frac{18+\sqrt{432}}{6}$$ we draw $$3$$ circles with equal radii, in such way that each of them are tangent to the other $$2$$ circles and to circle $$A$$. Inside the circle $$A$$ we draw a circle $$B$$ in such way that is tangent to each of the $$3$$ new circles. An equilateral triangle $$C$$ is inscribed in $$B$$.

If the area of $$C$$ can be written in the form:

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

Where $$a,b,c$$ and $$d$$ are integers such that $$b|a$$ and $$d|c$$.

Find:

$$a+b+c+d$$

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