Given a rhombus with diagonals a and b, which contains an inscribed circle. The task is to find the area of that circle in terms of a and b.
Examples:
Input: l = 5, b = 6
Output: 11.582Input: l = 8, b = 10
Output: 30.6341
Approach: From the figure, we see, the radius of inscribed circle is also a height h=OH of the right triangle AOB. To find it, we use equations for triangle’s area :
Area AOB = 1/2 * (a/2) * (b/2) = ab/8 = 12ch
where c = AB i.e. a hypotenuse. So,
r = h = ab/4c = ab/4?(a^2/4 + b^2/4) = ab/2?(a^2+b^2)
and therefore area of the circle is
A = ? * r^2 = ? a^2 b^2 /4(a2 + b2)
Below is the implementation of above approach:
C++
// C++ Program to find the area of the circle// which can be inscribed within the rhombus#include <bits/stdc++.h>using namespace std;// Function to find the area// of the inscribed circlefloat circlearea(float a, float b){ // the diagonals cannot be negative if (a < 0 || b < 0) return -1; // area of the circle float A = (3.14 * pow(a, 2) * pow(b, 2)) / (4 * (pow(a, 2) + pow(b, 2))); return A;}// Driver codeint main(){ float a = 8, b = 10; cout << circlearea(a, b) << endl; return 0;} |
Java
// Java Program to find the area of the circle // which can be inscribed within the rhombus public class GFG { // Function to find the area // of the inscribed circle public static float circlearea(double a, double b) { // the diagonals cannot be negative if (a < 0 || b < 0) return -1 ; //area of the circle float A = (float) ((3.14 * Math.pow(a, 2) * Math.pow(b, 2)) / (4 * (Math.pow(a, 2) + Math.pow(b, 2)))) ; return A ; } // Driver code public static void main(String[] args) { float a = 8, b = 10 ; System.out.println(circlearea(a, b)); }// This code is contributed by ANKITRAI1} |
Python 3
# Python 3 Program to find the area of the circle# which can be inscribed within the rhombus# Function to find the area# of the inscribed circledef circlearea(a, b): # the diagonals cannot be negative if (a < 0 or b < 0): return -1 # area of the circle A = ((3.14 * pow(a, 2) * pow(b, 2))/ (4 * (pow(a, 2) + pow(b, 2)))) return A# Driver codeif __name__ == "__main__": a = 8 b = 10 print( circlearea(a, b))# This code is contributed by ChitraNayal |
C#
// C# Program to find the area of the circle // which can be inscribed within the rhombususing System;public class GFG { // Function to find the area // of the inscribed circle public static float circlearea(double a, double b) { // the diagonals cannot be negative if (a < 0 || b < 0) return -1 ; //area of the circle float A = (float) ((3.14 * Math.Pow(a, 2) * Math.Pow(b, 2)) / (4 * (Math.Pow(a, 2) + Math.Pow(b, 2)))) ; return A ; } // Driver code public static void Main() { float a = 8, b = 10 ; Console.WriteLine(circlearea(a, b)); }// This code is contributed by inder_verma..} |
PHP
<?php// PHP Program to find the area // of the circle which can be // inscribed within the rhombus// Function to find the area// of the inscribed circlefunction circlearea($a, $b){ // the diagonals cannot be negative if ($a < 0 || $b < 0) return -1; // area of the circle $A = (3.14 * pow($a, 2) * pow($b, 2)) / (4 * (pow($a, 2) + pow($b, 2))); return $A;}// Driver code$a = 8; $b = 10;echo circlearea($a, $b);// This code is contributed by anuj_67?> |
Javascript
<script>// javascript Program to find the area of the circle // which can be inscribed within the rhombus // Function to find the area // of the inscribed circle function circlearea(a , b){ // the diagonals cannot be negative if (a < 0 || b < 0) return -1 ; //area of the circle var A = ((3.14 * Math.pow(a, 2) * Math.pow(b, 2)) / (4 * (Math.pow(a, 2) + Math.pow(b, 2)))) ; return A ;}// Driver codevar a = 8, b = 10 ;document.write(circlearea(a, b).toFixed(4));// This code is contributed by Amit Katiyar </script> |
Output:
30.6341
Time Complexity: O(1), as calculating squares using pow function is a constant time operation.
Auxiliary Space: O(1), as no extra space is required
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