# System of Circle-O-Triangle!

Geometry Level 5

There are 3 circles.

• First one has center at $$A \left(\dfrac{\sqrt{3}}{2},\ 0 \right)$$ and has radius $$1$$.

• Second one has center at $$B \left(\dfrac{20-3\sqrt{3}}{2},\ 1 \right)$$ and has radius $$3$$.

• Third one has center at $$C \left(5,\ 5\sqrt{3}-\dfrac{3}{2} \right)$$ and has radius $$2$$.

Find the perimeter of the triangle with maximum area, having one vertex on the circumference of each of the circles. Enter the answer to 3 decimal places.

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