# Harry Potter's Magical Geometry!

Geometry Level 4

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

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

If Area of red colored region can be expressed as:

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

Find $$a + b + c + d$$

Details and Assumptions:-

• Take $$\pi$$ as $$\dfrac{22}{7}$$.
×