# A geometry problem by Mohammad Hamdar

Geometry Level 5

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

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

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