# 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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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

 `// 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. `

## PHP

 ` `

Output:

`Area of square = 18`

Time Complexity: O(1)

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