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Knowing two points on a circle does not define a unique circle, so it is impossible to find the centre of the circle as there are infinitely many centres possible.

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What is a point from where the points on the circle are of equal distances?

That point is known as the "center of the circle". Every circle has one.


What is the set of points in a plane that are equidistant from a given point known as the center?

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What is it called when a line goes halfway across a circle?

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What are the set of all points in a plane that are the same distance from a given point called the center called?

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Centripetal Force is the answer :)