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This is actually a computer science question in that I need to create a program that will determine the center of a circle given $4$ points on its circumference.

Does anyone know the algorithm, theorem or method? I think it has something to do with cyclic quadrilaterals.

Thanks.

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2 Answers 2

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The perpendicular bisector of a chord of a circle goes through the center of the circle. Therefore, if you have two chords, then the perpendicular bisectors intersect at exactly the center of the circle. Here is a picture of what I'm describing.

So, given four points on the circle, draw chords between pairs of them, draw the perpendicular bisectors of the chords, and find the point of intersection.

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Three points are sufficient. Take two pairs of points which forms two chords of the circle. The perpendicular bisector of the chords will intersect at the center of the circle. It shouldn't be too difficult to convert this procedure to a program.

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