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If you take the generic equation for a circle, and make three equations out of it by

substituting the coordinates of the three points, you can solve them simultaneously

and derive a single solution for the center and radius of a circle. In other words, you

can always find one, and only one, circle that those three points lie on.

You have to be able to sing and dance pretty well in the key of algebra to do that, but

once you've done it, it feels great. Then your next exercise is to write a simple computer

program that takes the three points as an input, and outputs the center and radius of

the circle. We wrote that once, when we wanted a tool to explore the outline of the

Mandelbrot set. Totally useless, and loads of fun.

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14y ago

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Q: Why do any three noncollinear points lie on a circle?
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