The center of the circle. That's how the circle is defined. (The collection of all points on a plane equidistant from a fixed point. The fixed point is the center and the fixed distance is the radius.)
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It is the centre of the circle
Circle!
A circle.
Yes. A circle is defined as the set of all points in a plane equidistant from a given point (the center of the circle) - hence - all points of a circle must be co-planar by definition.
That set of points forms what is known as a "circle".