Harry Potter's Magical Geometry!

In the given figure , ΔABC\Delta ABC is an equilateral triangle with side as 1 unit.

The given circle is the in-circle of ΔABC\Delta ABC

If Area of red colored region can be expressed as:

abcd\dfrac{a\sqrt{b} - c}{d} where a,b,c,dNa,b,c,d\in \mathbb{N} ,bb is independent of a perfect square ,

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

Details and Assumptions:-

  • Take π\pi as 227\dfrac{22}{7}.

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