All geometric shapes can be inscribed in a circle, since the circle is bigger than the other geometric shape inscribed in it. (Obviously)
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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.
No, the circle is inscribed in the quadrilateral.
There are different formula for: Height, Area, Perimeter, Angle, Length of Median Radius of inscribed circle Perimeter of inscribed circle Area of inscribed circle etc.
Yes all inscribed angles in a circle have their vertex on the circumference of the circle. Central angles have their vertex at the center of the circle.
An inscribed circle, possibly.