# Star Stumper

Geometry Level 4

A square $$ABCD$$ of side length $$2$$ has a 4-pointed star inscribed in it - its points touch the midpoints of each side of the square, and it has lines of symmetry $$AC$$ and $$BD$$.

Given that the angle between the points is $$120^\circ$$, the area of the shaded region can be written as $$\dfrac { a-b\sqrt { 3 } }{ c }$$ where $$a$$, $$b$$ and $$c$$ are coprime. Find $$a+b+c$$.

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