If you want to, you can always draw a circle around an isosceles trapezoid and the radius can be half the base of the trapezoid.
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The area of a trapezium (trapezoid) is the product of: A: the perpendicular distance between the parallel sides b: half the sum of the lengths of the other two sides. The inscribed circle is irrelevant.
Yes.
yes.
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.
No, the circle is inscribed in the quadrilateral.