LightOJ 1331：求面积

Description

Agent J is preparing to steal an antique diamond piece from a museum. As it is fully guarded and they are guarding it using high technologies, it's not easy to steal the piece. There are three circular laser scanners in the museum which are the main headache for Agent J. The scanners are centered in a certain position, and they keep rotating maintaining a certain radius. And they are placed such that their coverage areas touch each other as shown in the picture below:

Here R₁, R₂ and R₃ are the radii of the coverage areas of the three laser scanners. The diamond is placed in the place blue shaded region as in the picture. Now your task is to find the area of this region for Agent J, as he needs to know where he should land to steal the diamond.

Input

Input starts with an integer T (≤ 1000), denoting the number of test cases.

Each case starts with a line containing three real numbers denoting R₁, R₂ and R₃ (0 < R₁, R₂, R₃ ≤ 100). And no number contains more than two digits after the decimal point.

Output

For each case, print the case number and the area of the place where the diamond piece is located. Error less than 10^-6 will be ignored.

Sample Input

3

1.0 1.0 1.0

2 2 2

3 3 3

Sample Output

Case 1: 0.16125448

Case 2: 0.645017923

Case 3: 1.4512903270

求出三条边  用余弦定理求出角度   三角形面积=1/2*a*b*sinC

#include<cstdio>
#include<cstring>
#include<cmath>
#include<queue>
#define pi acos(-1.0)
#include<algorithm>
using namespace std;
int main()
{
	int t;
	scanf("%d",&t);int ans=0;
	while(t--)
	{
		ans++;
	   double r1,r2,r3;
	   scanf("%lf%lf%lf",&r1,&r2,&r3);
	   double c=r1+r2;
	   double a=r2+r3;
	   double b=r1+r3;
	  double C=acos((a*a+b*b-c*c)/(2*a*b));
	  double A=acos((b*b+c*c-a*a)/(2*b*c));
	  double B=acos((a*a+c*c-b*b)/(2*a*c));
	  double s1=abs(pi*r1*r1*A/(pi*2));
	  double s2=abs(pi*r2*r2*B/(pi*2));
	  double s3=abs(pi*r3*r3*C/(pi*2));
	  double s=abs(sqrt(1-(a*a+b*b-c*c)/(2*a*b)*(a*a+b*b-c*c)/(2*a*b))*a*b/2);
	  printf("Case %d: %.6lf
",ans,s-s1-s2-s3);
	}
	return 0;
}