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No, the circle is inscribed in the quadrilateral.
no. if it did it wouldent be a circle a circle can circumscribe a right angle a right angle whose vertex lies on a circle has sides that intersect the circle's diameter.
circumcircle of a triangle is the circle that passes through all 3 vertices. this circle is said to be circumscribe the triangle
It is an inscribed quadrilateral or cyclic quadrilateral.
Yes and the diameter of the circle will be the diagonal of the rectangle.