The Vitruvian Triangle

Geometry Level 4

A square and circle with equal areas are placed in such a way that both intersected in some points like Vitruvian Man of Leonardo Da Vinci. One of the intersections is point A, located exactly on middle of square side (see illustration). Two other points, called B and C, are chosen from intersection points so that ABC triangle can be formed. If the area of square (or circle) is one unit, what is the area of ABC triangle?

(Enter approximation up to 3 digits on answer box)

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