hdu5476 Explore Track of Point（数学）

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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

10 1 -1 0 1 0

Sample Output

Case #1: 3.2214

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