pair<circle, circle> tangent_circles(const line& l, const line& m, double r) {
double th = arg(m.b - m.a) - arg(l.b - l.a);
double ph = (arg(m.b - m.a) + arg(l.b - l.a)) / 2.0;
point p = crosspointLL(l, m);
point d = polar(r / sin(th / 2.0), ph);
return mp(circle(p - d, r), circle(p + d, r));
}
// 左側切除
Polygon convex_cut(const Polygon &p, const Line &l){
Polygon res;
for(int i = 0; i < p.size(); ++i){
P a = curr(p,i), b = next(p,i);
Line tl = Line(a, b);
if(ccw(l[0], l[1], a) != -1) res.push_back(a);
if(ccw(l[0], l[1], a) * ccw(l[0], l[1], b) < 0)
res.push_back(crosspointLL(tl, l));
}
return res;
}
circle circum_circle(point a, point b, point c) {
point o = crosspointLL(bisector(a, b), bisector(a, c));
return circle(o, abs(a - o));
}
