Three 60 degree sectors of a unit circle pack neatly inside an equilateral triangle. The side length of this triangle can be written as $\displaystyle A+\frac{B}{\sqrt{C}}$, where $\displaystyle A, B, C$ are integers with $\displaystyle C$ square-free. What is the value of $\displaystyle A+B+C$? Anyone please help me.

Circles inside triangle (packing problem)-whatsapp-image-2018-12-19-8.18.16-pm-1-.jpeg