In a solid geometry problem, consider a right circular cone with a height of 12 units and a base radius of 5 units. An equilateral triangle is inscribed in a circle such that the circle is parallel to the base of the cone and the circle's plane is 9 units above the cone's base. Determine the side length of the equilateral triangle. Let's think step by step and output the final answer within \boxed{}.
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