这题求的是圆环相交的面积，画图可知 圆环相交面积=大交大-2×大交小+小交小
这题需要用到圆的相交面积公式
题目链接：http://acm.hust.edu.cn/vjudge/contest/view.action?cid=93642#problem/I
AC代码：
1 #include <stdio.h> 2 #include <string.h> 3 #include <math.h> 4 #include <algorithm> 5 #define exp 1e-10 6 #define PI 3.141592654 7 using namespace std; 8 typedef long long LL; 9 struct point 10 { 11 double x,y; 12 point(double x=0,double y=0):x(x),y(y){} 13 }a,b; 14 15 double dist(point a,point b) 16 { 17 double x=(a.x-b.x)*(a.x-b.x); 18 double y=(a.y-b.y)*(a.y-b.y); 19 return sqrt(x+y); 20 } 21 22 double overlap(point c1,double r1,point c2,double r2) 23 { 24 double d=dist(c1,c2); 25 if(r1+r2<d+exp) 26 { 27 return 0; 28 } 29 if(d<fabs(r1-r2)+exp) 30 { 31 double r=min(r1,r2); 32 return PI*r*r; 33 } 34 double x=(d*d+r1*r1-r2*r2)/(2*d); 35 double t1=acos(x/r1); 36 double t2=acos((d-x)/r2); 37 return r1*r1*t1+r2*r2*t2-d*r1*sin(t1); 38 } 39 40 int main() 41 { 42 int T,f; 43 f=0; 44 double r,R; 45 scanf("%d",&T); 46 while(T--) 47 { 48 f++; 49 scanf("%lf%lf",&r,&R); 50 scanf("%lf%lf%lf%lf",&a.x,&a.y,&b.x,&b.y); 51 double big=overlap(a,R,b,R); 52 double bigsmall=overlap(a,R,b,r); 53 double small=overlap(a,r,b,r); 54 printf("Case #%d: %.6lf ",f,big-2*bigsmall+small); 55 } 56 return 0; 57 }