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how to find the center of an arc given start and end points

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@user3310: An arc of a circle is defined by three non-colinear points. – Américo Tavares Nov 9 '10 at 14:58
Another way of phrasing Américo's statement: you can't determine a radius from just start and end points. – J. M. Nov 9 '10 at 15:34

circles through 2 points

As Américo Tavares and J. M. said in their comments, two points do not uniquely determine an arc. Shown above are several circles that pass through two given points. However, the center of any circle that passes through those two points is on the perpendicular bisector of the line segment with those points as endpoints.

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Did those circles just move? ;-) – Aryabhata Nov 10 '10 at 22:49

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