A geometry problem by Mohammad Hamdar

Geometry Level 5

Consider a circle CC with center OO and radius R=3R=3. ABCABC is a triangle inscribed in CC such that BC=5BC = 5 and ABC=60\angle ABC = 60^\circ .

Given that the area of the triangle ABCABC is equal to ab(a+c)d \dfrac{a\sqrt b(a + \sqrt c)}d , where a,b,ca,b,c and dd are positive integers with b,cb,c square-free and dd minimized. Find a+b+c+da+b+c+d.

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