Area of square Circumscribed by Circle (original) (raw)

Last Updated : 2 Sep, 2024

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 * r 2
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 * r 2

CPP `

// C++ program to find Area of // square Circumscribed by Circle #include 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;

}

Java

// 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.

Python3

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.

C#

// 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.

JavaScript

PHP

`

Output:

Area of square = 18

**Time Complexity: O(1)
**Auxiliary Space: O(1)
Please suggest if someone has a better solution which is more efficient in terms of space and time.