# 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 * 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 d^{2}= a^{2}+ a^{2}

d = 2 * a^{2}

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)

= d^{2}/ 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 <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;` `}` |

## 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

`<?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.` `?>` |

## Javascript

`<script>` `// Javascript 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` ` ` `let r = 3;` ` ` ` ` `// Call Function to find` ` ` `// an area of square` ` ` `document.write(` `" Area of square = "` ` ` `+ find_Area(r));` ` ` `// This code is contributed by Mayank Tyagi` `</script>` |

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.

This article is contributed by **Aarti_Rathi**. Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above

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