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Calculus Level 2

Let SS be the maximum possible area of a right triangle that can be drawn in a semi-circle of radius 11, where one of the legs (and not the hypotenuse) of the triangle must lie on the diameter of the semicircle.

If S=abc,S = \dfrac{a\sqrt{b}}{c}, where a,ca,c are positive coprime integers and bb is a positive square-free integer, find a+b+c.a + b + c.

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