Expected Area of a Triangle

Calculus Level pending

It is widely known that a triangle inscribed in a semicircle with the base of the triangle being the diameter of the semicircle is always a right triangle.

\(A\) and \(B\) are the endpoints of the diameter of a circle with radius \(1.\) Point \(C\) is a point chosen with equal probability along the circumference of the circle. The expected area of \(\Delta ABC\) is \(N.\) What is \(\lfloor 100N \rfloor\text{?}\)

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