If the two triangles above are congruent, equilateral triangles, which is greater, the total area of the three \(\color{red}{\text{red}}\) regions or the total area of the six \(\color{purple}{\text{purple}}\) regions?

The circle in figure A is tangent to all sides of the triangle. The center circle of figure B is tangent to the other three circles, which are themselves tangent to the sides of the triangle; those four circles are all congruent.

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