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# lightoj1385 - Kingdom Division

1385 - Kingdom Division PDF (English) Statistics Forum Time Limit: 1 second(s) Memory Limit: 32 MB The king of Geometry-Land was in deep trouble. His three sons quarrel all the time. The king tried a lot but in vain. How about dividing the

1385 - Kingdom Division
 PDF (English) Statistics Forum
 Time Limit: 1 second(s) Memory Limit: 32 MB

The king of Geometry-Land was in deep trouble. His three sons quarrel all the time. The king tried a lot but in vain. "How about dividing the kingdom?" the king thought to himself. So, he called the advisors and described his plan. They opened the map...

The kingdom is triangular. The king denoted the three vertices as A, B, C. He drew a line from B to E (E is any point in segment AC) and another line from C to F (F is any point in segment AB). The intersection of BE and CF was denoted by X.

Then they got four parts - a (triangle BFX), b (triangle BCX), c (triangle CEX) and d (quadrilateral AEXF). The king decided to give these areas - a, b, c to his three sons. And the area d would be the king's new kingdom.

Now, you are given the value of a, b and c. You have to find the area of d.

# Input

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

Each case starts with a line containing three positive real numbers a b and c which are not greater than 1000. You can also assume that the numbers contain at most four places after the decimal point.

# Output

For each case, print the case number first. Then if the area of d cannot be determined, print "-1". Otherwise print the area of d. Errors less than 10-6 will be ignored.

# Output for Sample Input

4

1 2 1

2 4 2

1 3 3

1.28 2.67 3.12

Case 1: 2

Case 2: 4

Case 3: 5

Case 4: 12.4063611138

```#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cstring>
#include<algorithm>
#include<cmath>
#include<queue>
#include<list>
#include<vector>
#define eps 1e-6
using namespace std;
int main()
{
int t,test=1;
double a,b,c;
scanf("%d",&t);
while(t--){
scanf("%lf%lf%lf",&a,&b,&c);
double x=a/b*c;
printf("Case %d: ",test++);
if(b-x<eps){
printf("-1\n");
}
else {
double y=(x+c)*(a+x)/(b-x);
printf("%.7lf\n",x+y);
}
}
return 0;
} ```

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