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.