# Radius of the circle when the width and height of an arc is given

Given a circle in which the width and height of an arc are given. The task is to find the radius of the circle with the help of the width and height of the arc.
Examples:

```Input: d = 4, h = 1
Output: The radius of the circle is 2.5

Input: d = 14, h = 8
Output: The radius of the circle is 7.0625```

Approach

• Let the radius of the circle be r
• Let the height and width of the arc be h & d
• Now, the diameter DC bisects the chord AB in two halves, each having length d/2
• Also the diameter is divided by the chord in two parts, the part inside arc h and the remaining 2r-h
• Now from intersecting chords theorem
h*(2r-h) = (d/2)^2
or, 2rh – h^2 = d^2/4
so, r = d^2/8h + h/2
• So, radius of the circle

## C++

 `// C++ program to find` `// radius of the circle` `// when the width and height` `// of an arc is given`   `#include ` `using` `namespace` `std;`   `// Function to find the radius` `void` `rad(``double` `d, ``double` `h)` `{` `    ``cout << ``"The radius of the circle is "` `        ``<< ((d * d) / (8 * h) + h / 2)` `        ``<< endl;` `}`   `// Driver code` `int` `main()` `{` `    ``double` `d = 4, h = 1;` `    ``rad(d, h);` `    ``return` `0;` `}`

## Java

 `// Java program to find` `// radius of the circle` `// when the width and height` `// of an arc is given` `class` `GFG` `{`   `// Function to find the radius` `static` `void` `rad(``double` `d, ``double` `h)` `{` `    ``System.out.println( ``"The radius of the circle is "` `        ``+ ((d * d) / (``8` `* h) + h / ``2``));` `}`   `// Driver code` `public` `static` `void` `main(String[] args)` `{` `    ``double` `d = ``4``, h = ``1``;` `    ``rad(d, h);` `}` `}`   `/* This code contributed by PrinciRaj1992 */`

## Python3

 `# Python3 program to find` `# radius of the circle` `# when the width and height` `# of an arc is given`   `# Function to find the radius` `def` `rad(d, h):` `    ``print``(``"The radius of the circle is"``,` `        ``((d ``*` `d) ``/` `(``8` `*` `h) ``+` `h ``/` `2``))`   `# Driver code` `d ``=` `4``; h ``=` `1``;` `rad(d, h);`   `# This code is contributed by 29AjayKumar`

## C#

 `// C# program to find` `// radius of the circle` `// when the width and height` `// of an arc is given` `using` `System;`   `class` `GFG` `{`   `// Function to find the radius` `static` `void` `rad(``double` `d, ``double` `h)` `{` `    ``Console.WriteLine( ``"The radius of the circle is "` `        ``+ ((d * d) / (8 * h) + h / 2));` `}`   `// Driver code` `public` `static` `void` `Main()` `{` `    ``double` `d = 4, h = 1;` `    ``rad(d, h);` `}` `}`   `// This code is contributed by AnkitRai01`

## PHP

 ``

## Javascript

 ``

Output:

`The radius of the circle is 2.5`

Time Complexity: O(1)

Auxiliary Space: O(1)

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