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 / √2and 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 <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. ?> |
Output:
Area of square = 18
Time Complexity: O(1)
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Improved By : vt_m
