Programa para hallar la Circunferencia de cualquier polígono regular

Dado un polígono de n lados con longitud de lado a . La tarea es encontrar el área del circuncírculo del polígono.

Ejemplos:

Input: n = 10, a = 3
Output: 1.99737

Input: n = 5, a = 6
Output: 3.02487

Enfoque : un n -ágono regular divide el círculo en n partes, por lo que el ángulo central del triángulo es un círculo completo dividido por n : 360 grados/n . 
Aplicando la ley de los cosenos para las longitudes de los tres lados del triángulo, obtenemos

c2 = a2 + b2 - 2ab cos C 
or, a2 = r2 + r2 - 2rr cos (360/n) 
or, a2 = 2r2 - 2r2 cos (360/n) 
or, c2 = r2 (2 - 2 cos (360/n)) 
so, a=r√(2-2cos(360/n))

Therefore, 
r=a/√(2-2cos(360/n)) 

A continuación se muestra la implementación del enfoque anterior: 

// C++ Program to find the radius
// of the circumcircle of the given polygon
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the radius
// of the circumcircle
float findRadiusOfcircumcircle(float n, float a)
{
 
    // these cannot be negative
    if (n < 0 || a < 0)
        return -1;
 
    // Radius of the circumcircle
    float radius = a / sqrt(2 - (2 * cos(360 / n)));
 
    // Return the radius
    return radius;
}
 
// Driver code
int main()
{
 
    float n = 5, a = 6;
 
    // Find the radius of the circumcircle
    cout << findRadiusOfcircumcircle(n, a) << endl;
 
    return 0;
}

// Java Program to find the radius
// of the circumcircle of the given polygon
 
import java.io.*;
 
class GFG {
   
// Function to find the radius
// of the circumcircle
static float findRadiusOfcircumcircle(float n, float a)
{
 
    // these cannot be negative
    if (n < 0 || a < 0)
        return -1;
 
    // Radius of the circumcircle
    float radius = (float)(a / Math.sqrt(2 - (2 * Math.cos(360 / n))));
 
    // Return the radius
    return radius;
}
 
// Driver code
 
    public static void main (String[] args) {
        float n = 5, a = 6;
 
    // Find the radius of the circumcircle
    System.out.println( findRadiusOfcircumcircle(n, a)) ;
 
    }
}
// This code is contributed
// by anuj_67..

# Python3 Program to find the
# radius of the circumcircle
# of the given polygon
 
# from math import all methods
from math import *
 
# Function to find the radius
# of the circumcircle
def findRadiusOfcircumcircle(n, a) :
 
    # these cannot be negative
    if n < 0 or a < 0 :
        return -1
 
    # Radius of the circumcircle
    radius = a / sqrt(2 - (2 * cos(360 / n)))
 
    # Return the radius
    return radius
 
# Driver code
if __name__ == "__main__" :
 
    n , a = 5, 6
 
    # Find the radius of the circumcircle
    print(round(findRadiusOfcircumcircle(n, a), 5))
 
# This code is contributed
# by ANKITRAI1

// C# Program to find the radius
// of the circumcircle of the given polygon
using System;
 
class GFG
{
 
// Function to find the radius
// of the circumcircle
static float findRadiusOfcircumcircle(float n,
                                      float a)
{
 
    // these cannot be negative
    if (n < 0 || a < 0)
        return -1;
 
    // Radius of the circumcircle
    float radius = (float)(a / Math.Sqrt(2 -
                   (2 * Math.Cos(360 / n))));
 
    // Return the radius
    return radius;
}
 
// Driver code
public static void Main ()
{
    float n = 5, a = 6;
 
    // Find the radius of the circumcircle
    Console.WriteLine(findRadiusOfcircumcircle(n, a));
}
}
 
// This code is contributed
// by anuj_67

<?php
// PHP Program to find the radius
// of the circumcircle of the
// given polygon
 
// Function to find the radius
// of the circumcircle
function findRadiusOfcircumcircle($n, $a)
{
 
    // these cannot be negative
    if ($n < 0 || $a < 0)
        return -1;
 
    // Radius of the circumcircle
    $radius = $a / sqrt(2 - (2 *
                    cos(360 / $n)));
 
    // Return the radius
    return $radius;
}
 
// Driver code
$n = 5;
$a = 6;
 
// Find the radius of the circumcircle
echo findRadiusOfcircumcircle($n, $a);
 
// This code is contributed by Anuj_67..
?>

<script>
// javascript Program to find the radius
// of the circumcircle of the given polygon
 
// Function to find the radius
// of the circumcircle
function findRadiusOfcircumcircle(n , a)
{
 
    // these cannot be negative
    if (n < 0 || a < 0)
        return -1;
 
    // Radius of the circumcircle
    var radius = (a / Math.sqrt(2 - (2 * Math.cos(360 / n))));
 
    // Return the radius
    return radius;
}
 
// Driver code
var n = 5, a = 6;
 
// Find the radius of the circumcircle
document.write( findRadiusOfcircumcircle(n, a).toFixed(5)) ;
 
 
// This code is contributed by shikhasingrajput
</script>

3.02487

Tiempo Complejidad: O(1)
Espacio Auxiliar: O(1)