/*---------------------------------------------------------------*/
/*  Program chapter4_3                                           */
/*                                                               */
/*  This program reads the coordinates of three points and then  */
/*  references a function to determine the coordinates of the    */
/*  center of a circle through the points and the radius of the  */
/*  circle.                                                      */

#include <stdio.h>
#include <math.h>

int main(void)
{
   /*  Declare variables.  */
   double x1, x2, x3, y1, y2, y3, m12, xc, yc, r;
   double circle_x_coord(double x1,double y1,double x2,double y2,
                         double x3,double y3);

   /*  Get user input from the keyboard.  */
   printf("Enter x and y coordinates for first point: \n");
   scanf("%lf %lf",&x1,&y1);
   printf("Enter x and y coordinates for second point: \n");
   scanf("%lf %lf",&x2,&y2);
   printf("Enter x and y coordinates for third point: \n");
   scanf("%lf %lf",&x3,&y3);

   /*  Use a function to determine the x coordinate of the center.  */
   xc = circle_x_coord(x1,y1,x2,y2,x3,y3);

   /*  Compute the y coordinate of the center.  */
   m12 = (y2 - y1)/(x2 - x1);
   yc = -(1/m12)*(xc - (x1 + x2)/2) + (y1 + y2)/2;

   /*  Compute the radius of the circle.  */
   r = sqrt((x1 - xc)*(x1 - xc) + (y1 - yc)*(y1 - yc));

   /*  Print circle parameters.  */
   printf("\nCenter of Circle: (%.1f,%.1f) \n",xc,yc);
   printf("Radius of Circle: %.1f \n",r);

   /*  Exit program.  */
   return 0;
}
/*---------------------------------------------------------------*/
/*  This function computes the x coordinate of the center of a   */
/*  circle given three points on the circle.                     */

double circle_x_coord(double x1,double y1,double x2,double y2,
                      double x3,double y3)
{
   /*  Declare variables.  */
   double m12, m23, xc_num, xc_den, xc;

   /*  Compute slopes of the two lines between points.  */
   m12 = (y2 - y1)/(x2 - x1);
   m23 = (y3 - y2)/(x3 - x2);

   /*  Compute the x coordinate of the center of the circle.  */
   xc_num = m12*m23*(y1 - y3) + m23*(x1 + x2) - m12*(x2 + x3);
   xc_den = 2*(m23 - m12);
   xc = xc_num/xc_den;

   /*  Return the x coordinate of the center.  */
   return xc;
}
/*---------------------------------------------------------------*/