Find the area

Geometry Level 5

A circle with centre O1{ O }_{ 1 } and radius 2r2r is drawn. A point O2{ O }_{ 2 } is taken at a distance rr from O1{ O }_{ 1 }. Now a circle is drawn with centre O2{ O }_{ 2 } and radius rr. Now two lines are drawn from O2{ O }_{ 2 } each making an angle 600{ 60 }^{ 0 } with O1{ O }_{ 1 }O2{ O }_{ 2 } produced and the given figure is obtained.

If the area of the shaded region in the given figure can be written as A=kr2A=k{r}^{2} then find 100k\left\lfloor 100k \right\rfloor .

Note: The starting part of the question is just a description of how the figure is drawn. The figure must be taken as the reference for finding the shaded region.

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