What is the algorithm for finding the center of a circle from three points?

Question

I have three points on the circumference of a circle: pt A = (A.x, A.y); pt B = (B.x, B.y); pt C = (C.x, C.y); How do I calculate the center of the circle?

Answer 1

You can create a system of equations.

name your center as (x,y)

A(2,1) B(3,4) C(5,-2)

Now set the squared distance from (x,y) to A = to the squared distance from (x,y) to B

Now repeat with B and C

You end up creating a system of 2 equations with 2 unknowns

2x+6y=20

6x-6y =24

8x = 44

x= 5.5

y = 1.5