Yes, you can draw a circle through the four points of a trapezoid, because the four points of the trapezoid can be equidistant from one point, making that distance the radius.
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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.
A diameter is a line connecting any two points in a circle that passes through the centre of a circle. You can draw 1 diameter and divide the circle in half. You can draw 2 and divide it into 4 pieces or draw an infinite amount and divide it into infinite pieces.
draw a circle
Construct a circle with a compass and then draw a straight line through its centre
Draw two diameters of the circle and join the points where they meet the circumference.