Area of square Circumscribed by Circle

Given the radius(r) of circle then find the area of square which is Circumscribed by circle.

Examples:

Input : r = 3
Output :Area of square = 18

Input :r = 6
Output :Area of square = 72

All four sides of a square are of equal length and all four angles are 90 degree. The circle is circumscribed on a given square shown by a shaded region in the below diagram.



Properties of Circumscribed circle are as follows:

  • The center of the circumcircle is the point where the two diagonals of a square meet.
  • Circumscribed circle of a square is made through the four vertices of a square.
  • The radius of a circumcircle of a square is equal to the radius of a square.

Formula used to calculate the area of circumscribed square is:
2 * r2
where, r is the radius of the circle in which a square is circumscribed by circle.

How does this formula work?

Assume diagonal of square is d and length of side is a.

We know from the Pythagoras Theorem, the diagonal of a
square is √(2) times the length of a side.
i.e d2 = a2 + a2
d = 2 * a2
d = √(2) * a
Now,
a = d / √2

and We know diagonal of square that are Circumscribed by
Circle is equal to Diameter of circle.
so Area of square = a * a
= d / √(2) * d / √(2)
= d2/ 2
= ( 2 * r )2/ 2 ( We know d = 2 * r )
= 2 * r2

CPP

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// C++ program to find Area of
// square Circumscribed by Circle
#include <iostream>
using namespace std;
  
// Function to find area of square
int find_Area(int r)
{
    return (2 * r * r);
}
  
// Driver code
int main() 
{
    // Radius of a circle
    int r = 3;
      
    // Call Function to find 
    // an area of square
    cout << " Area of square = " 
                 << find_Area(r);
      
    return 0;
}

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Java

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// Java program to find Area of
// square Circumscribed by Circle
class GFG {
      
    // Function to find area of square
    static int find_Area(int r)
    {
        return (2 * r * r);
    }
      
    // Driver code
    public static void main(String[] args)
    {
        // Radius of a circle
        int r = 3;
  
        // Call Function to find
        // an area of square
        System.out.print(" Area of square = "
                             + find_Area(r));
    }
}
  
// This code is contributed by Anant Agarwal.

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Python3

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# Python program to
# find Area of
# square Circumscribed
# by Circle
  
# Function to find
# area of square
def find_Area(r):
  
    return (2 * r * r)
      
# driver code
# Radius of a circle
r = 3
      
# Call Function to find 
# an area of square
print(" Area of square = ", find_Area(r))
  
# This code is contributed
# by Anant Agarwal.

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C#

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// C# program to find Area of
// square Circumscribed by Circle
using System;
  
class GFG {
      
    // Function to find area of square
    static int find_Area(int r)
    {
        return (2 * r * r);
    }
      
    // Driver code
    public static void Main()
    {
        // Radius of a circle
        int r = 3;
  
        // Call Function to find
        // an area of square
        Console.WriteLine(" Area of square = "
                            + find_Area(r));
    }
}
  
// This code is contributed by vt_m.

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PHP

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<?php
// PHP program to find Area of
// square Circumscribed by Circle
  
// Function to find area of square
function find_Area( $r)
{
    return (2 * $r * $r);
}
  
    // Driver code
    // Radius of a circle
    $r = 3;
      
    // Call Function to find 
    // an area of square
    echo ("Area of square = ");
    echo(find_Area($r));
      
// This code is contributed by vt_m.
?>

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Output:

Area of square = 18

Time Complexity: O(1)



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Improved By : vt_m