Program to find Circumcenter of a Triangle in C++

In this tutorial, we will be discussing a program to find the circumcenter of a triangle.

For this we will be provided with three noncollinear points. Our task is to find the circumcenter of the triangle formed by those points.

Example

 Live Demo

#include <iostream>
#include <cfloat>
using namespace std;
//storing X and Y values
#define pdd pair<double, double>
void lineFromPoints(pdd P, pdd Q, double &a, double &b, double &c){
   a = Q.second - P.second;
   b = P.first - Q.first;
   c = a*(P.first)+ b*(P.second);
}
void perpendicularBisectorFromLine(pdd P, pdd Q, double &a, double &b, double &c){
   pdd mid_point = make_pair((P.first + Q.first)/2, (P.second + Q.second)/2);
   c = -b*(mid_point.first) + a*(mid_point.second);
   double temp = a;
   a = -b;
   b = temp;
}
pdd lineLineIntersection(double a1, double b1, double c1, double a2, double b2, double c2){
   double determinant = a1*b2 - a2*b1;
   if (determinant == 0){
      return make_pair(FLT_MAX, FLT_MAX);
   } else {
      double x = (b2*c1 - b1*c2)/determinant;
      double y = (a1*c2 - a2*c1)/determinant;
      return make_pair(x, y);
   }
}
void findCircumCenter(pdd P, pdd Q, pdd R){
   double a, b, c;
   lineFromPoints(P, Q, a, b, c);
   double e, f, g;
   lineFromPoints(Q, R, e, f, g);
   perpendicularBisectorFromLine(P, Q, a, b, c);
   perpendicularBisectorFromLine(Q, R, e, f, g);
   pdd circumcenter = lineLineIntersection(a, b, c, e, f, g);
   if (circumcenter.first == FLT_MAX && circumcenter.second == FLT_MAX){
      cout << "The two perpendicular bisectors "
         "found come parallel" << endl;
      cout << "Thus, the given points do not form "
         "a triangle and are collinear" << endl;
   } else {
      cout << "The circumcenter of the triangle PQR is: ";
      cout << "(" << circumcenter.first << ", "
         << circumcenter.second << ")" << endl;
   }
}
int main(){
   pdd P = make_pair(6, 0);
   pdd Q = make_pair(0, 0);
   pdd R = make_pair(0, 8);
   findCircumCenter(P, Q, R);
   return 0;
}

Output

The circumcenter of the triangle PQR is: (3, 4)