define Point on circle
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A point circle has radius zero and only includes a single point - the centre of the circle. A real/imaginary circle concerns whether the radius of the circle is real or imaginary. If the radius of a circle is imaginary then there are no real points on the circle.
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If the distance between a point P and the center O of a circle is greater then the radius of the circle, the point is outside the circle. If the distance between a point P and the center O of a circle is equal to the radius of the circle, the point is on the circle.
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