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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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How many planes can be drawn through any three noncollinear points in a plane?
just one
Are three noncollinear points always contained in only one plane?
Yes a plane can always be drawn three any three points, whether they are linear or not.
Noncollinear points lie on the same line?
You have to have three or more points to have non-colinear points because any two points determine a line. Noncolinear are NOT on the same line.
Can two points be noncollinear?
No. Any two points can be made to form a line.
Can noncollinear parts lie on the same plane?
Yes. In fact any three points that are not collinear define a plane and therefore MUST lie on a plane.
