#include<tuple>
#include<cmath>

struct Vector {
    double x;
    double y;
    
    Vector operator-(const Vector r) const {
        return {x - r.x, y - r.y};
    }
    
    Vector operator+(const Vector r) const {
        return {x + r.x, y + r.y};
    }
    
    Vector operator*(double r) const {
        return {x*r, y*r};
    }
    
    Vector operator/(double r) const {
        return {x/r, y/r};
    }
    
    double operator*(const Vector r) const {
        return x * r.x + y * r.y;
    }
};

Vector get_intersection(std::pair<Vector, Vector> l1, std::pair<Vector, Vector> l2) {
    Vector d1 = l1.second - l1.first;
    Vector d2 = l2.second - l2.first;
    Vector n2 = Vector({d2.y, -d2.x}) / std::hypot(d2.y, -d2.x);  // Normal of the second line
    
    double h = (l1.first - l2.first) * n2; // height of the first point of l1 on vector l2
    double hd = d1 * n2;  // height differential of the vector that defines l1
    
    const double threshold = 0.0f;  // A threshold where height differential is considered to correspond to parallel lines
    if(std::abs(hd) <= threshold) {
        return {NAN, NAN};
    }
    return l1.first + d1 * (h / -hd);
}

int main() {
    std::pair<Vector, Vector> l1 = {Vector({1, 2}), Vector({5, 1})};
    std::pair<Vector, Vector> l2 = {Vector({3, 7}), Vector({6, 2})};
    Vector intersection = get_intersection(l2, l1);

    return 0;
}