POJ-2242 The Circumference of the Circle-已知三点共圆求周长

The Circumference of the Circle

Time Limit: 1000MS Memory Limit: 65536KTotal Submissions: 7850 Accepted: 4768

Description

To calculate the circumference of a circle seems to be an easy task - provided you know its diameter. But what if you don't? 

You are given the cartesian coordinates of three non-collinear points in the plane. 
Your job is to calculate the circumference of the unique circle that intersects all three points. 

Input

The input will contain one or more test cases. Each test case consists of one line containing six real numbers x1,y1, x2,y2,x3,y3, representing the coordinates of the three points. The diameter of the circle determined by the three points will never exceed a million. Input is terminated by end of file.

Output

For each test case, print one line containing one real number telling the circumference of the circle determined by the three points. The circumference is to be printed accurately rounded to two decimals. The value of pi is approximately 3.141592653589793.

Sample Input

0.0 -0.5 0.5 0.0 0.0 0.50.0 0.0 0.0 1.0 1.0 1.05.0 5.0 5.0 7.0 4.0 6.00.0 0.0 -1.0 7.0 7.0 7.050.0 50.0 50.0 70.0 40.0 60.00.0 0.0 10.0 0.0 20.0 1.00.0 -500000.0 500000.0 0.0 0.0 500000.0

Sample Output

3.144.446.2831.4262.83632.243141592.65

Source

Ulm Local 1996

//利用已知三角形三边求其面积的公式和正弦定理求得圆的直径#include <iostream>#include <cstring>#include <iomanip>#include <stdio.h>#include <cmath>const double PI=acos(-1.0);using namespace std;int main(){    double x1,y1,x2,y2,x3,y3,a,b,c,s,p,d;    while(cin>>x1>>y1>>x2>>y2>>x3>>y3)    {        a=sqrt((x3-x2)*(x3-x2)+(y3-y2)*(y3-y2));        b=sqrt((x1-x3)*(x1-x3)+(y1-y3)*(y1-y3));        c=sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));        p=(a+b+c)/2;        s=sqrt(p*(p-a)*(p-b)*(p-c));        d=a*b*c/(2*s);        cout<<setiosflags(ios::fixed)<<setprecision(2)<<d*PI<<endl;    }    return 0;}