hdu5476 Explore Track of Point（数学）

思路：一道纯平面几何题....显然AM是成立的，然后猜测剩下的是与AB,AC相切的圆的劣弧...就做完了...

#include<bits/stdc++.h>
using namespace std;
double dis(double x1,double y1,double x2,double y2)
{
    return sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));
}
int main()
{
    int T,cas=1;
    scanf("%d",&T);
    while(T--)
    {
        printf("Case #%d: ",cas++);
        double ax,ay,bx,by,cx,cy;
        scanf("%lf%lf%lf%lf%lf%lf",&ax,&ay,&bx,&by,&cx,&cy);
        double mx = (cx+bx)/2;
        double my = (cy+by)/2;
        double am = dis(ax,ay,mx,my);
        double r = dis(bx,by,mx,my)/dis(ax,ay,mx,my)*dis(ax,ay,bx,by);
        double ang = atan(dis(ax,ay,bx,by)/r);
        printf("%.4f\n",am+2*ang*r);  
    }
}

Problem Description

In Geometry, the problem of track is very interesting. Because in some cases, the track of point may be beautiful curve. For example, in polar Coordinate system,ρ=cos3θ is like rose, ρ=1−sinθ is a Cardioid, and so on. Today, there is a simple problem about it which you need to solve.

Give you a triangle ΔABC and AB = AC. M is the midpoint of BC. Point P is in ΔABC and makes min{∠MPB+∠APC,∠MPC+∠APB} maximum. The track of P is Γ. Would you mind calculating the length of Γ?

Given the coordinate of A, B, C, please output the length of Γ.

 

Input

There are T (1≤T≤104) test cases. For each case, one line includes six integers the coordinate of A, B, C in order. It is guaranteed that AB = AC and three points are not collinear. All coordinates do not exceed 104 by absolute value.

 

Output

For each case, first please output "Case #k: ", k is the number of test case. See sample output for more detail. Then, please output the length of Γ with exactly 4 digits after the decimal point.

 

Sample Input

1
0 1 -1 0 1 0

 

Sample Output

Case #1: 3.2214