UVa - 10991 - Region

#include <iostream>
#include <algorithm>
#include <cmath>
#include <iomanip>
#define pi acos(-1.0)
using namespace std;

int main(){
    double r1, r2, r3;
    double t1, t2, t3;
    double porishima, area_triangle, angle_circle1, angle_circle2, angle_circle3;
    int t;
    cin >> t;
    while(t--){
        cin >> r1 >> r2 >> r3;
        t1 = r2 + r3; t2 = r1 + r3; t3 = r1 + r2;

        porishima = (t1+t2+t3) / 2;
        area_triangle = sqrt(porishima * (porishima-t1) * (porishima-t2) * (porishima-t3));

        angle_circle1 = acos((t2*t2+t3*t3-t1*t1)/(2*t2*t3));
        angle_circle2 = acos((t1*t1+t3*t3-t2*t2)/(2*t1*t3));
        angle_circle3 = (pi - (angle_circle1 + angle_circle2));
        double area_circle = angle_circle1*r1*r1 + angle_circle2*r2*r2 + angle_circle3*r3*r3;
        cout << fixed << setprecision(6) << area_triangle  - area_circle/2 << endl;

    }

    return 0;
}