Задача с Codeforces

#include <iostream>
#include <cmath>
 
using namespace std;
 
const double PI = acos(-1.0);
const double eps = 1e-4;
 
struct pi
{
    double x, y;
};
 
istream &operator >>(istream &in, pi &p)
{
    in >> p.x >> p.y;
    return in;
}
double len(pi a, pi b)
{
    return sqrt((b.x - a.x) * (b.x - a.x) + (b.y - a.y) * (b.y - a.y));
}
 
double gcd(double a, double b) {
    while (fabs(a) > eps && fabs(b) > eps) {
        if (a > b)
                a -= floor(a / b) * b;
        else
                b -= floor(b / a) * a;
    }
    return a + b;
}
 
int main()
{
    pi p1, p2, p3;
    cin >> p1 >> p2 >> p3;
 
    double a, b, c, s, A, B, C, R, S, n;
 
    a = len(p1, p2);
    b = len(p2, p3);
    c = len(p1, p3);
    s = abs(((p2.x - p1.x) * (p3.y - p1.y) - (p3.x - p1.x) * (p2.y - p1.y)) / 2);
    R = (a * b * c) / (4 * s);
    A = acos((b * b + c * c - a * a) / (2 * b * c));
    B = acos((a * a + c * c - b * b) / (2 * a * c));
    C = acos((a * a + b * b - c * c) / (2 * a * b));
    n = PI / gcd(gcd(A, B), C);
    S = abs((n / 2) * R * R * sin(2 * PI / n));
 
    cout.precision(10);
 
    cout << fixed << S;
 
    return 0;
}