# 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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