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Suppose we have three complex numbers $a_1,a_2,a_3$ which are non-collinear. What is the best way to find the center of the circle that contains these three points ?

  • It would be done the same way as finding the circumcenter of a triangle from 3 coordinate points. – turkeyhundt Feb 12 '15 at 01:03
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    I have no idea why they related the other is different question –  Feb 12 '15 at 01:08
  • contains = all 3 points on the circumference? what guarantees it exists? – benji Feb 12 '15 at 01:09
  • You can think of the complex number as a pair of coordinates, no? Then you could do it the same way as the linked question. – turkeyhundt Feb 12 '15 at 01:15
  • I notice that if $a_3$ moves around while $a_1$ and $a_2$ stay fixed, then the center moves along a line although $a_3$ moves about in a plane. That rules out any possibility of the center being any sort of analytic function of $a_1,a_2,a_3$. ${}\qquad{}$ – Michael Hardy Feb 12 '15 at 03:29

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Find the equation of the perpendicular bisectors of a pair of lines(any pair) of the triangle formed by connecting the points. The intersection of these bisectors will be the center of the circle.

user26334
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