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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.)

Q: What is a point that is equidistant from all points on a circle?

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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".

Related questions

The center of the circle.

It is the centre of the circle

All points on the circumference of a circle drawn on a plane are equidistant from the single point on the plane which is the center of the circle.

THE center

Circle!

the center

A circle.

The centre of a circle.

The center of a circle is the point from which all points on the circle are equidistant.

Circle

A circle is the locus of all points equidistant from a given point, which is the center of the circle, and a circle can be drawn with a compass. (The phrase "locus of points for a circle" does not seem to be conventionally defined.) or true

All points equidistant from a center point.