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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Michael Fuller by Michael Fuller
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