Normally it's its centre which is at the mid point of its diameter.
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An angle does not have a mid point.
It is the center of the circle
The point from which the circle is drawn IS the center.
A circle has a round shape in which every point on the circle is the same distance from one point called "the center". The center of a circle is not on the circle.
It is the mid-point of a line segment that has end points