#include <math.h>
#define eps 1e-8
struct point{double x,y;};

double xmult(point p1,point p2,point p0){
	return (p1.x-p0.x)*(p2.y-p0.y)-(p2.x-p0.x)*(p1.y-p0.y);
}

double distance(point p1,point p2){
	return sqrt((p1.x-p2.x)*(p1.x-p2.x)+(p1.y-p2.y)*(p1.y-p2.y));
}

double disptoline(point p,point l1,point l2){
	return fabs(xmult(p,l1,l2))/distance(l1,l2);
}

point intersection(point u1,point u2,point v1,point v2){
	point ret=u1;
	double t=((u1.x-v1.x)*(v1.y-v2.y)-(u1.y-v1.y)*(v1.x-v2.x))
			/((u1.x-u2.x)*(v1.y-v2.y)-(u1.y-u2.y)*(v1.x-v2.x));
	ret.x+=(u2.x-u1.x)*t;
	ret.y+=(u2.y-u1.y)*t;
	return ret;
}

//判直線和圓相交,包括相切
int intersect_line_circle(point c,double r,point l1,point l2){
	return disptoline(c,l1,l2)<r+eps;
}

//判線段和圓相交,包括端點和相切
int intersect_seg_circle(point c,double r,point l1,point l2){
	double t1=distance(c,l1)-r,t2=distance(c,l2)-r;
	point t=c;
	if (t1<eps||t2<eps)
		return t1>-eps||t2>-eps;
	t.x+=l1.y-l2.y;
	t.y+=l2.x-l1.x;
	return xmult(l1,c,t)*xmult(l2,c,t)<eps&&disptoline(c,l1,l2)-r<eps;
}

//判圓和圓相交,包括相切
int intersect_circle_circle(point c1,double r1,point c2,double r2){
	return distance(c1,c2)<r1+r2+eps&&distance(c1,c2)>fabs(r1-r2)-eps;
}

//計算圓上到點p最近點,如p與圓心重合,返回p本身
point dot_to_circle(point c,double r,point p){
	point u,v;
	if (distance(p,c)<eps)
		return p;
	u.x=c.x+r*fabs(c.x-p.x)/distance(c,p);
	u.y=c.y+r*fabs(c.y-p.y)/distance(c,p)*((c.x-p.x)*(c.y-p.y)<0?-1:1);
	v.x=c.x-r*fabs(c.x-p.x)/distance(c,p);
	v.y=c.y-r*fabs(c.y-p.y)/distance(c,p)*((c.x-p.x)*(c.y-p.y)<0?-1:1);
	return distance(u,p)<distance(v,p)?u:v;
}

//計算直線與圓的交點,保證直線與圓有交點
//計算線段與圓的交點可用這個函數后判點是否在線段上
void intersection_line_circle(point c,double r,point l1,point l2,point& p1,point& p2){
	point p=c;
	double t;
	p.x+=l1.y-l2.y;
	p.y+=l2.x-l1.x;
	p=intersection(p,c,l1,l2);
	t=sqrt(r*r-distance(p,c)*distance(p,c))/distance(l1,l2);
	p1.x=p.x+(l2.x-l1.x)*t;
	p1.y=p.y+(l2.y-l1.y)*t;
	p2.x=p.x-(l2.x-l1.x)*t;
	p2.y=p.y-(l2.y-l1.y)*t;
}

//計算圓與圓的交點,保證圓與圓有交點,圓心不重合
void intersection_circle_circle(point c1,double r1,point c2,double r2,point& p1,point& p2){
	point u,v;
	double t;
	t=(1+(r1*r1-r2*r2)/distance(c1,c2)/distance(c1,c2))/2;
	u.x=c1.x+(c2.x-c1.x)*t;
	u.y=c1.y+(c2.y-c1.y)*t;
	v.x=u.x+c1.y-c2.y;
	v.y=u.y-c1.x+c2.x;
	intersection_line_circle(c1,r1,u,v,p1,p2);
}