Let $S_1,S_2$ and $S_3$ be three circles of unit radius which touch each other externally. The common tangent to each pair of circles are drawn and extended so that they  can intersect and form a triangle $ABC$ with circumradius $R,$ then $R$ is equal to

  • A

    $4+2\sqrt 3$

  • B

    $2(1+\frac{1}{\sqrt 3})$

  • C

    $4(1+\sqrt 3)$

  • D

    $\frac{3(1+\sqrt 3)}{2}$

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