圆外接圆的面积

给定圆的半径(r)，然后找到由圆外接的正方形的面积。
例子：

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

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

正方形的所有四个边的长度相等，并且所有四个角度均为90度。圆在下图的阴影区域所示的给定正方形上外接。

外接圆的属性如下：

• 外接圆的中心是正方形的两个对角线相交的点。
• 正方形的外接圆是通过正方形的四个顶点构成的。
• 正方形的外接圆的半径等于正方形的半径。

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.

Javascript

// 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

输出：

Area of square = 18

时间复杂度：O(1)