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三分house到shop的距离，二分这条斜边到cinema的距离

#include<stdio.h>
#include<string.h>
#include<iostream>
#include<algorithm>
#include<math.h>
#include<set>
#include<queue>
#include<vector>
#include<map>
using namespace std;
#define ll int
#define N 90
#define Pi 3.1415926535898
#define eps 1e-10
double t1, t2;
struct node{
	double x,y;
}c,h,s;
double dist(double x1,double y1,double x2,double y2){
	return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
double dist(node a,node b){
	return sqrt((a.x-b.x)*(a.x-b.x)+(a.y-b.y)*(a.y-b.y));
}
double work(double du){
	node x = {s.x*(1-du) + h.x*du, s.y*(1-du)+h.y*du};
	double ac = dist(x,c), as = dist(x,s), ah = dist(x,h);
	if(ac+ah<=t2&&ac+as<=t1)return min(t2-ah,t1-as);
	double l = 0, r = 1.0;
	for(int i = 1; i <= 300 ; i++){
		double mid = (l+r)/2;
		node b = {c.x*(1-mid)+x.x*mid,c.y*(1-mid)+x.y*mid};
		double bc = dist(b,c), bs = dist(b, s), bh = dist(b, h);
		if(bc+bh<=t2 && bc+bs<=t1) l = mid;
		else r = mid;
	}
	node b = {c.x*(1-l)+x.x*l, c.y*(1-l)+x.y*l};
	return dist(b,c);
}
int main(){  
	ll i, j, u, v;
	while(cin>>t1>>t2){
		cin>>c.x>>c.y;
		cin>>h.x>>h.y;
		cin>>s.x>>s.y;
		double a = dist(c,s), b = dist(c,h), c = dist(h,s);
		
		if(b+t2>=a+c){printf("%.8lf\n",min(a+t1+c,b+t2));continue;}
		t1+=a+eps; t2+=b+eps;
		double l = 0, r = 1.0, ans = 0;
		for(i = 1; i <= 300; i++){
			double mid1 = (l+r)/2.0, mid2 = (mid1+r)/2.0;
			double ans1 = work(mid1), ans2 = work(mid2);
			if(ans1<ans2) l = mid1;
			else r = mid2;
			ans = max(ans, max(ans1,ans2));
		}
		printf("%.8lf\n",ans);
	}
	return 0;
}