Circles all around

Geometry Level 3

Three equal circles of radius 1 unit touches each other. Radius of the circle touching all the three circles is :

(A) \( \frac{ 2 - \sqrt{3} }{ \sqrt{3} } \)

(B) \( \frac{ \sqrt{3} - \sqrt{2} }{ \sqrt{2} } \)

(C) \( \frac{ 2 + \sqrt{3} }{ \sqrt{3} } \)

(D) \( \frac{ \sqrt{3} + \sqrt{2} }{ \sqrt{2} } \)

This problem is a part of the sets - 3's & 4's & " G " for geometry
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