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

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```

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 ` `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

 ``

Javascript

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Output:

`1.28624`

Time complexity: O(logn) as it is using inbuilt sqrt  function

Auxiliary Space: O(1) since using constant variables

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