ZOJ-1090-The Circumference of the Circle(计算几何，海伦公式，三角形外接圆半径公式，cout输出小数的一些问题)

The Circumference of the Circle

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Time Limit: 1 Second      Memory Limit: 32768 KB

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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 Specification

The input file 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 Specification

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

给出圆上的三点求圆的周长，给出的三点构成圆的内接三角形，可以求出三角形三边的长度，由海伦公式可以求出三角形面积：

已知三角形三边a,b,c，则 
　　p=(a+b+c)/2
　　S=√[p(p-a)(p-b)(p-c)] 

已知三角形面积可以由三角形外接圆半径公式求出外接圆的半径：

由正弦定理，a/sinA=b/sinB=c/sinC=2R,得sinA=a/(2R),又三角形面积公式Ｓ=(bcsinA)/2,所以S=(abc)/(4R),故R=(abc)/(4S).
然后即可求出圆的周长
#include <iostream>#include <cmath>#include <iomanip>using namespace std;const double pi=3.141592653589793;int main(){double x1,y1,x2,y2,x3,y3,a,b,c,st,cir,r,p;while(cin>>x1>>y1>>x2>>y2>>x3>>y3){a=sqrt((x1-x2)*(x1-x2)+(y1-y2)*(y1-y2));b=sqrt((x1-x3)*(x1-x3)+(y1-y3)*(y1-y3));c=sqrt((x3-x2)*(x3-x2)+(y3-y2)*(y3-y2));p=(a+b+c)/2;st=sqrt(p*(p-a)*(p-b)*(p-c));//三角形面积，海伦公式r=a*b*c/(4*st);cir=2*pi*r;cout.setf(ios::fixed);cout.precision(2);cout<<cir<<endl;}return 0;}
cout.setf(ios::fixed);不设置为定点小数的话，cout.precision(2)指的是有效位数为2，如3.1；
 设置为定点小数后，cout.precision(2)指的是小数有效位数为2，如3.14