An equilateral triangle of minimum area contains six congruent circles with radii each equal to one unit. Each side of the triangle is tangent to three circles.

    In other words, the circles form a triangular-like pattern and fit perfectly within an equilateral triangle.

    What are the exact lengths of the sides of the equilateral triangle?

    Credit will be awarded on the following guidelines:

• Proper use of mathematics, and
• A detailed explanation that accompanies the work.

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