question_answer

Three equal circles each of diameter d are drawn on a plane in such a way that each circle touches the other two circles. A big circle is drawn in such a manner that it touches each of the small circles internally. The area of the big circle is

A)  \[\pi \,{{d}^{2}}\]                              

B)  \[\pi \,{{d}^{2}}\,\,{{(2-\sqrt{3})}^{2}}\]

C)  \[\frac{\pi {{d}^{2}}\,{{(\sqrt{3}+1)}^{2}}}{2}\]      

D)  \[\frac{\pi {{d}^{2}}\,{{(\sqrt{3}+2)}^{2}}}{12}\]

E)  None of these