1 #include <iostream>
2 #include <stdio.h>
3 #include <string.h>
4 #include <stdlib.h>
5 #include <algorithm>
6 using namespace std;
7 typedef long long ll;
8 const int maxn = 1e3+10;
9 const double INF = 0x3f3f3f3f;
10 const double eps = 1e-10;
11 const double PI = acos(-1.0);
12 int dcmp(double k) {return k<-eps?-1:k>eps?1:0;}
13 double sqr(double x) {return x*x;}
14 double mysqrt(double n) {return sqrt(max(0.0,n));}
15
16 struct point{
17 double x,y;
18 point (double x=0, double y=0):x(x),y(y){}
19 };
20
21 typedef point Vector;
22
23 point res[maxn];
24 double r;
25 int n;
26
27 Vector operator +(Vector A,Vector B) {return Vector(A.x+B.x,A.y+B.y); }
28 Vector operator -(Vector A,Vector B) {return Vector(A.x-B.x,A.y-B.y); }
29 Vector operator *(Vector A,double p) {return Vector(A.x*p,A.y*p); }
30 Vector operator /(Vector A,double p) {return Vector(A.x/p,A.y/p); }
31 double dot(const point &a, const point &b) {return a.x*b.x+a.y*b.y;}
32 double cross(const point &a, const point &b) {return a.x*b.y-a.y*b.x;}
33 double abs(const point &o) {return sqrt(dot(o,o));}
34
35 point crosspt(const point &a, const point &b, const point &p, const point &q)
36 {
37 double a1 = cross(b-a,p-a);
38 double a2 = cross(b-a,q-a);
39 return (p*a2-q*a1)/(a2-a1);
40 }
41
42 void circle_cross_line(point a,point b,point o,double r,point ret[],int &num)
43 {
44 double x0 = o.x,y0 = o.y;
45 double x1 = a.x,y1 = a.y;
46 double x2 = b.x,y2 = b.y;
47 double dx = x2-x1, dy = y2-y1;
48 double A = dx*dx+dy*dy;
49 double B = 2*dx*(x1-x0)+2*dy*(y1-y0);
50 double C = sqr(x1-x0) + sqr(y1-y0) -sqr(r);
51 double delta = B*B-4*A*C;
52 num = 0;
53 if(dcmp(delta)>=0)
54 {
55 double t1 = (-B-mysqrt(delta))/(2*A);
56 double t2 = (-B+mysqrt(delta))/(2*A);
57 if(dcmp(t1-1)<=0 && dcmp(t1)>=0)
58 {
59 ret[num++] = point(x1+t1*dx,y1+t1*dy);
60 }
61 if(dcmp(t2-1)<=0 && dcmp(t2)>=0)
62 {
63 ret[num++] = point(x1+t2*dx,y1+t2*dy);
64 }
65 }
66 }
67
68 double sector_area(const point &a, const point &b)
69 {
70 double theta = atan2(a.y,a.x)-atan2(b.y,b.x);
71 while(theta<=0) theta += 2*PI;
72 while(theta>2*PI) theta -= 2*PI;
73 theta = min(theta,2*PI-theta);
74 return r*r*theta/2;
75 }
76
77 double calc(const point &a, const point &b)
78 {
79 point p[2];
80 int num=0;
81 int ina = dcmp(abs(a)-r)<0;
82 int inb = dcmp(abs(b)-r)<0;
83 if(ina)
84 {
85 if(inb)
86 {
87 return fabs(cross(a,b))/2.0;
88 }
89 else
90 {
91 circle_cross_line(a,b,point(0,0),r,p,num);
92 return sector_area(b,p[0])+fabs(cross(a,p[0]))/2.0;
93 }
94 }
95 else
96 {
97 if(inb)
98 {
99 circle_cross_line(a,b,point(0,0),r,p,num);
100 return sector_area(p[0],a)+fabs(cross(p[0],b))/2.0;
101 }
102 else
103 {
104 circle_cross_line(a,b,point(0,0),r,p,num);
105 if(num==2)
106 {
107 return sector_area(a,p[0])+sector_area(p[1],b)+fabs(cross(p[0],p[1])) / 2.0;
108 }
109 else
110 {
111 return sector_area(a,b);
112 }
113 }
114 }
115 }
116
117 //计算多边形和圆相交的面积，半径为r，圆心为圆点，n边形，n个点顺序存在ret[0~n-1]中，ret[n]=ret[0]
118 double area()
119 {
120 double ret = 0;
121 for(int i=0;i<n;i++)
122 {
123 int sgn = dcmp(cross(res[i],res[i+1]));
124 ret += sgn*calc(res[i],res[i+1]);
125 // if(sgn>0) ret += calc(res[i],res[i+1]);
126 // else ret -= calc(res[i],res[i+1]);
127 }
128 return fabs(ret);
129 }
130
131 point p[maxn];
132 int m;
133 double P,Q;
134 double allArea;//多边形面积
135
136 //顺时针逆时针均可
137 double Area()
138 {
139 double ans = 0.0;
140 for(int i=0;i<n;i++)
141 {
142 ans = ans + cross(p[i+1],p[i]);
143 }
144 return fabs(ans/2);
145 }
146
147
148 int main()
149 {
150 scanf("%d",&n);
151 for(int i=0;i<n;i++)
152 {
153 double x,y;
154 scanf("%lf %lf",&x,&y);
155 p[i] = point(x,y);
156 a[n-i-1] = point(x,y);
157 }
158 p[n].x=p[0].x,p[n].y=p[0].y;
159
160 allArea = Area();
161 //printf("%.12f\n",allArea);
162
163 scanf("%d",&m);
164 for(int i=1;i<=m;i++)
165 {
166 double x,y;
167 scanf("%lf %lf %lf %lf",&x,&y,&P,&Q);
168
169 point tmp = point(x,y);
170 double goal = (1.-P/Q)*allArea;
171
172 for(int i=0;i<=n;i++)
173 {
174 res[i] = p[i]-tmp;
175 }
176
177 double left = 0,right = 1e5;
178 while(right-left>eps)
179 {
180 double mid = (right+left)*.5;
181 r = mid;
182
183 double Area = area();
184 if(Area<goal) left = mid;
185 else right = mid;
186 }
187 printf("%.12f\n",right);
188 }
189 }
