10432 - Polygon inside a circle/10432.cpp

   1 #include <iostream>
   2 #include <cstdlib>
   3 #include <cmath>
   4 #include <cassert>
   5
   6 using namespace std;
   7
   8 const double pi = 2*acos(0);
   9
  10 int main(){
  11   double r;
  12   int n;
  13   while (cin >> r >> n){
  14     assert(r > 0);
  15     assert(n > 2);
  16     double anguloInterno = (pi - (2*pi / n)); // 180 - (360/n)
  17     anguloInterno /= 2;
  18     //cout << anguloInterno * 180.0 / pi << endl;
  19     double anguloFaltante = pi - 2*anguloInterno;
  20     //cout << anguloFaltante * 180.0 / pi << endl;
  21     double b = r * sin(anguloFaltante) / sin(anguloInterno);
  22     //cout << b << endl;
  23     double h = r*r - b*b/4;
  24     h = sqrt(h);
  25     double resultado = b*h/2 * n;
  26     printf("%.3f\n", resultado);
  27   }
  28   return 0;
  29 }