Infinite Geometrical Geometric Series!

Geometry Level 4

Above figure consists of  circles\color{#3D99F6}{\infty \text{ circles}} inscribed in an Equilateral Triangle\color{#3D99F6}{\text{Equilateral Triangle}} in a pattern as shown above. Let Area of Infinite circles=A1\color{#3D99F6}{\text{Area of Infinite circles} = A_1}(dotted region)(\text{dotted region}) and Area of Equilateral Triangle ΔABC=A2\color{#3D99F6}{\text{Area of Equilateral Triangle } \Delta ABC= A_2}.

Find value of A1A2\color{#3D99F6}{\frac{A_1}{A_2}}. If your answer is of form πx\color{#3D99F6}{\frac{\pi}{\sqrt{x}}}, enter answer as x\color{#3D99F6}{x}.


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