Skip to content
Related Articles

Related Articles

Improve Article
Save Article
Like Article

Radius of the biggest possible circle inscribed in rhombus which in turn is inscribed in a rectangle

  • Last Updated : 18 Mar, 2021

Give a rectangle with length l & breadth b, which inscribes a rhombus, which in turn inscribes a circle. The task is to find the radius of this circle.
Examples: 
 

Input: l = 5, b = 3
Output: 1.28624

Input: l = 6, b = 4
Output: 1.6641

 

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the DSA Self Paced Course at a student-friendly price and become industry ready.  To complete your preparation from learning a language to DS Algo and many more,  please refer Complete Interview Preparation Course.

In case you wish to attend live classes with experts, please refer DSA Live Classes for Working Professionals and Competitive Programming Live for Students.

 



Approach: From the figure, it is clear that diagonals, x & y, are equal to the length and breadth of the rectangle. 
Also radius of the circle, r, inside a rhombus is = xy/2√(x^2+y^2). 
So, radius of the circle in terms of l & b is = lb/2√(l^2+b^2).
Below is the implementation of the above approach
 

C++




// C++ implementation of above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the radius
// of the inscribed circle
float circleradius(float l, float b)
{
 
    // the sides cannot be negative
    if (l < 0 || b < 0)
        return -1;
 
    // radius of the circle
    float r = (l * b) / (2 * sqrt((pow(l, 2) + pow(b, 2))));
    return r;
}
 
// Driver code
int main()
{
    float l = 5, b = 3;
    cout << circleradius(l, b) << endl;
 
    return 0;
}

Java




// Java implementation of above approach
 
import java.io.*;
 
class GFG {
     
// Function to find the radius
// of the inscribed circle
static float circleradius(float l, float b)
{
 
    // the sides cannot be negative
    if (l < 0 || b < 0)
        return -1;
 
    // radius of the circle
    float r = (float)((l * b) / (2 * Math.sqrt((Math.pow(l, 2) + Math.pow(b, 2)))));
    return r;
}
 
    // Driver code
    public static void main (String[] args) {
        float l = 5, b = 3;
    System.out.print (circleradius(l, b)) ;
    }
}
// This code is contributed by inder_verma..

Python3




# Python 3 implementation of
# above approach
from math import sqrt
 
# Function to find the radius
# of the inscribed circle
def circleradius(l, b):
     
    # the sides cannot be negative
    if (l < 0 or b < 0):
        return -1
 
    # radius of the circle
    r = (l * b) / (2 * sqrt((pow(l, 2) +
                             pow(b, 2))));
    return r
 
# Driver code
if __name__ == '__main__':
    l = 5
    b = 3
    print("{0:.5}" . format(circleradius(l, b)))
 
# This code is contribute
# by Surendra_Gagwar

C#




// C# implementation of above approach
using System;
 
class GFG
{
     
// Function to find the radius
// of the inscribed circle
static float circleradius(float l,
                          float b)
{
 
    // the sides cannot be negative
    if (l < 0 || b < 0)
        return -1;
 
    // radius of the circle
    float r = (float)((l * b) /
              (2 * Math.Sqrt((Math.Pow(l, 2) +
                   Math.Pow(b, 2)))));
    return r;
}
 
// Driver code
public static void Main ()
{
    float l = 5, b = 3;
    Console.WriteLine(circleradius(l, b));
}
}
 
// This code is contributed
// by inder_verma

PHP




<?php
// PHP implementation of above approach
 
// Function to find the radius
// of the inscribed circle
function circleradius($l, $b)
{
 
    // the sides cannot be negative
    if ($l < 0 || $b < 0)
        return -1;
 
    // radius of the circle
    $r = ($l * $b) / (2 * sqrt((pow($l, 2) +
                                pow($b, 2))));
    return $r;
}
 
// Driver code
$l = 5;
$b = 3;
echo circleradius($l, $b), "\n";
 
// This code is contributed by ajit
?>

Javascript




<script>
// javascript implementation of above approach
 
// Function to find the radius
// of the inscribed circle
function circleradius(l , b)
{
 
    // the sides cannot be negative
    if (l < 0 || b < 0)
        return -1;
 
    // radius of the circle
    var r = ((l * b) / (2 * Math.sqrt((Math.pow(l, 2) + Math.pow(b, 2)))));
    return r;
}
 
var l = 5, b = 3;
document.write(circleradius(l, b).toFixed(5)) ;
 
// This code is contributed by shikhasingrajput
</script>
Output: 
1.28624

 




My Personal Notes arrow_drop_up
Recommended Articles
Page :