2D (Circle)

struct Circle: Point {
    double r;
    Circle(double x = 0, double y = 0, double r = 0): Point(x, y), r(r) {}
    Circle(Point p, double r): Point(p), r(r) {}
    bool contains(Point p) {
        return ( * this - p).len() <= r + EPS;
    }
};
double sqr(double a) {
    return a * a;
}
void tangents(Point c, double r1, double r2, vector < Line > & ans) {
    double r = r2 - r1;
    double z = sqr(c.x) + sqr(c.y);
    double d = z - sqr(r);
    if (d < -EPS) return;
    d = sqrt(fabs(d));
    Line l((c.x * r + c.y * d) / z, (c.y * r - c.x * d) / z, r1);
    ans.push_back(l);
}
vector < Line > tangents(Circle a, Circle b) {
    vector < Line > ans;
    ans.clear();
    for (int i = -1; i <= 1; i += 2)
        for (int j = -1; j <= 1; j += 2)
            tangents(b - a, a.r * i, b.r * j, ans);
    for (int i = 0; i < ans.size(); ++i)
        ans[i].c -= ans[i].a * a.x + ans[i].b * a.y;
    vector < Line > ret;
    for (int i = 0; i < ans.size(); ++i) {
        bool ok = true;
        for (int j = 0; j < ret.size(); ++j)
            if (areSame(ret[j], ans[i])) {
                ok = false;
                break;
            }
        if (ok) ret.push_back(ans[i]);
    }
    return ret;
}
vector < Point > intersection(Line l, Circle cir) {
    double r = cir.r, a = l.a, b = l.b, c = l.c + l.a * cir.x + l.b * cir.y;
    vector < Point > res;
    double x0 = -a * c / (a * a + b * b), y0 = -b * c / (a * a + b * b);
    if (c * c > r * r * (a * a + b * b) + EPS) return res;
    else if (fabs(c * c - r * r * (a * a + b * b)) < EPS) {
        res.push_back(Point(x0, y0) + Point(cir.x, cir.y));
        return res;
    } else {
        double d = r * r - c * c / (a * a + b * b);
        double mult = sqrt(d / (a * a + b * b));
        double ax, ay, bx, by;
        ax = x0 + b * mult;
        bx = x0 - b * mult;
        ay = y0 - a * mult;
        by = y0 + a * mult;
        res.push_back(Point(ax, ay) + Point(cir.x, cir.y));
        res.push_back(Point(bx, by) + Point(cir.x, cir.y));
        return res;
    }
}
double cir_area_solve(double a, double b, double c) {
    return acos((a * a + b * b - c * c) / 2 / a / b);
}
double cir_area_cut(double a, double r) {
    double s1 = a * r * r / 2;
    double s2 = sin(a) * r * r / 2;
    return s1 - s2;
}
double commonCircleArea(Circle c1, Circle c2) {
    if (c1.r < c2.r) swap(c1, c2);
    double d = (c1 - c2).len();
    if (d + c2.r <= c1.r + EPS) return c2.r * c2.r * PI;
    if (d >= c1.r + c2.r - EPS) return 0.0;
    double a1 = cir_area_solve(d, c1.r, c2.r);
    double a2 = cir_area_solve(d, c2.r, c1.r);
    return cir_area_cut(a1 * 2, c1.r) + cir_area_cut(a2 * 2, c2.r);
}
bool areIntersect(Circle u, Circle v) {
    if (cmp((u - v).len(), u.r + v.r) > 0) return false;
    if (cmp((u - v).len() + v.r, u.r) < 0) return false;
    if (cmp((u - v).len() + u.r, v.r) < 0) return false;
    return true;
}
vector < Point > circleIntersect(Circle u, Circle v) {
    vector < Point > res;
    if (!areIntersect(u, v)) return res;
    double d = (u - v).len();
    double alpha = acos((u.r * u.r + d * d - v.r * v.r) / 2.0 / u.r / d);
    Point p1 = (v - u).rotate(alpha);
    Point p2 = (v - u).rotate(-alpha);
    res.push_back(p1 / p1.len() * u.r + u);
    res.push_back(p2 / p2.len() * u.r + u);
    return res;
}