Don't pay attention to special cases where the points are repeated or aligned. We will treat these cases in the future.
To solve this problem we must solve a system with three equations and three variables: The distance between the three points and the circunference center is equal to the circunference radius.
r^2 = (x1-x)^2 + (y1-y)^2 r^2 = (x2-x)^2 + (y2-y)^2 r^2 = (x3-x)^2 + (y3-y)^2where r is the circunference radius, and (x,y) is the circunference center.
The solution of this equation system is:
y = (a*f-c*d)/(b*d-a*e) x = y*b/a +c/a r = sqrt((x1-x)^2 + (y1-y)^2)where a, b, c, d, e and f are auxiliary variables:
a = 2*(x2-x1) b = 2*(y2-y1) c = x1*x1 + y1*y1 - x2*x2 - y2*y2 d = 2*(x3-x1) e = 2*(y3-y1) f = x1*x1 + y1*y1 - x3*x3 - y3*y3Then, write a program that implements these expressions and prints the value of r, x and y.