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Area of largest Circle that can be inscribed in a SemiCircle

  • Last Updated : 08 Apr, 2021

Given a semicircle with radius R, the task is to find the area of the largest circle that can be inscribed in the semicircle.
Examples: 
 

Input: R = 2
Output: 3.14

Input: R = 8
Output: 50.24

 

Approach: Let R be the radius of the semicircle
 

  1. For Largest circle that can be inscribed in this semicircle, the diameter of the circle must be equal to the radius of the semi-circle. 
     
  2. So, if the radius of the semi-circle is R, then the diameter of the largest inscribed circle will be R.
  3. Hence the radius of the inscribed circle must be R/2
  4. Therefore the area of the largest circle will be 
     
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
  1.  

 



Below is the implementation of the above approach: 
 

C++




// 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




// 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




# 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#




// 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

Javascript




<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));
 
// Thid code is contributed by rutvik_56.
</script>
Output: 
3.14

 

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