Circles 32 Hard 3 Triangles inscribed Geometry GC

Circles 32 Hard 3 Triangles inscribed Geometry GC

Three identical tangent circles are inscribed within an equilateral triangle, as shown above. What is the ratio of the areas of one circle to that of the triangle? A. π:(6+4√3) B. π:(6+2√3) C. π:(3+2√3) D. π:(1+√3) E. 3π:(6+4√3)