That looks like a moon!

Geometry Level 3

A semi circle of diameter 1 unit sits at the top of a semi circle of diameter 2 units. the shaded region inside the the semi circle but outside the larger semi circle is called a lune. If the area of the lune is \(\alpha\), then find the value of \[\lfloor 1000\alpha\rfloor\]


Note

  • Assume that the diameters are parallel to each other.
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