# 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 \(a+b+c+d\).