Conics and calculus

Calculus Level 4

In an isosceles triangle whose non-equal side is equal to the corresponding altitude, each being 2. Let the maximum area of the ellipse inscribed in the triangle whose one axis is along the altitude can be represented as \(\dfrac { A\pi }{ B\sqrt { C } } \), where \(A\) and \(B\) are coprime positive integers and \(C\) is square-free. Find the value of \(A+B+C\).

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