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All geometric shapes can be inscribed in a circle, since the circle is bigger than the other geometric shape inscribed in it. (Obviously)
No. For example, if one angle measures 100 degrees, and its adjacent angle is 80 degrees, then the opposite angles would be either 200 or 160 degrees, but in order for a quadrilateral to be inscribed in a circle the opposite angles would have to equal 180 degrees. A parallelogram can be inscribed in a circle if it is a rectangle.
rectangle
No, because there is no acute angle in a circle.
yes ...all the angles of the triangle must touch a spot on the circle..