UVa 11731 - Ex-circles

链接

传送门

题意

给出一个三角形和它的三个旁切圆，求指定部分的面积。具体见原题。

思路

利用旁切圆半径公式即可。

代码

#include <cstdio>
#include <cstring>
#include <algorithm>
#include <cmath>

using namespace std;

double Area(double a, double b, double c) {
  double p = (a + b + c) / 2;
  return sqrt(p * (p - a) * (p - b) * (p - c));
}

double Ang(double a, double b, double c) {
  return acos((c * c - a * a - b * b) / (2 * a * b));
}

int main() {
  int a, b, c, t = 0;
  while (~scanf("%d%d%d", &a, &b, &c) && (a || b || c)) {
    double S = Area(a, b, c);
    double ra = 2 * S / (-a + b + c);
    double rb = 2 * S / (a - b + c);
    double rc = 2 * S / (a + b - c);
    double A = Ang(b, c, a);
    double B = Ang(a, c, b);
    double C = Ang(a, b, c);
    double ans1 = S + (a * ra + b * rb + c * rc) / 2;
    double ans2 = A * ra * ra + B * rb * rb + C * rc * rc;
    printf("Case %d: %.2f %.2f\n", ++t, ans1, ans2 / 4);
  }
  return 0;
}