Find the area

Geometry Level 5

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

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

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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