Área del Círculo más grande que se puede inscribir en un Semicírculo

Dado un semicírculo de radio R , la tarea es encontrar el área del círculo más grande que se puede inscribir en el semicírculo.
Ejemplos: 
 

Input: R = 2
Output: 3.14

Input: R = 8
Output: 50.24

Aproximación : Sea R el radio del semicírculo
 

1. Para el círculo más grande que se puede inscribir en este semicírculo, el diámetro del círculo debe ser igual al radio del semicírculo. 
    
2. Entonces, si el radio del semicírculo es R , entonces el diámetro del círculo inscrito más grande será R .
3. Por lo tanto, el radio del círculo inscrito debe ser R/2
4. Por lo tanto, el área del círculo más grande será 
    

Area of circle = pi*Radius2
               = pi*(R/2)2

since the radius of largest circle is R/2
where R is the radius of the semicircle

A continuación se muestra la implementación del enfoque anterior: 
 

// C++ Program to find the biggest circle
// which can be inscribed within the semicircle
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the area
// of the circle
float circlearea(float R)
{
 
    // Radius cannot be negative
    if (R < 0)
        return -1;
 
    // Area of the largest circle
    float a = 3.14 * R * R / 4;
 
    return a;
}
 
// Driver code
int main()
{
    float R = 2;
    cout << circlearea(R) << endl;
 
    return 0;
}

// Java Program to find the biggest circle
// which can be inscribed within the semicircle
class GFG
{
     
    // Function to find the area
    // of the circle
    static float circlearea(float R)
    {
     
        // Radius cannot be negative
        if (R < 0)
            return -1;
     
        // Area of the largest circle
        float a = (float)((3.14 * R * R) / 4);
     
        return a;
    }
     
    // Driver code
    public static void main (String[] args)
    {
        float R = 2;
        System.out.println(circlearea(R));
    }
}
 
// This code is contributed by AnkitRai01

# Python3 Program to find the biggest circle
# which can be inscribed within the semicircle
 
# Function to find the area
# of the circle
def circlearea(R) :
 
    # Radius cannot be negative
    if (R < 0) :
        return -1;
 
    # Area of the largest circle
    a = (3.14 * R * R) / 4;
 
    return a;
 
# Driver code
if __name__ == "__main__" :
 
    R = 2;
    print(circlearea(R)) ;
     
# This code is contributed by AnkitRai01

// C# Program to find the biggest circle
// which can be inscribed within the semicircle
using System;
 
class GFG
{
     
    // Function to find the area
    // of the circle
    static float circlearea(float R)
    {
     
        // Radius cannot be negative
        if (R < 0)
            return -1;
     
        // Area of the largest circle
        float a = (float)((3.14 * R * R) / 4);
     
        return a;
    }
     
    // Driver code
    public static void Main (string[] args)
    {
        float R = 2;
        Console.WriteLine(circlearea(R));
    }
}
 
// This code is contributed by AnkitRai01

<script>
 
// Javascript Program to find the biggest circle
// which can be inscribed within the semicircle
 
// Function to find the area
// of the circle
function circlearea(R)
{
 
    // Radius cannot be negative
    if (R < 0)
        return -1;
 
    // Area of the largest circle
    var a = 3.14 * R * R / 4;
 
    return a;
}
 
// Driver code
var R = 2;
document.write(circlearea(R));
 
// This code is contributed by rutvik_56.
</script>

3.14

Complejidad de tiempo : O(1)

Espacio Auxiliar: O(1)