Radii of the three tangent circles of equal radius which are inscribed within a circle of given radius

Given here is a circle of a given radius. Inside it, three tangent circles of equal radius are inscribed. The task is to find the radii of these tangent circles.**Examples:**

Input:R = 4Output:1.858Input:R = 11Output::5.1095

**Approach**:

- Let the radii of the tangent circles be
**r**, and the radius of the circumscribing circle

is**R**.**x**is the smaller distance from the circumference of the tangent circle and the center of the circumscribing circle. - From the diagram, it is very clear,
**2r + x = R** - now in triangle
**OBC**,**cos 30 = r/(r+x)****rcos30 + xcos30 = r****x = r(1-cos30)/cos30** - also,
**x = R-2r** - So,
**R-2r = r(1-cos30)/cos30****R-2r = 0.133r/0.867****R-2r = 0.153r****R = 2.153r**

so,**r = 0.4645R**

## C++

`// C++ program to find the radii` `// of the three tangent circles` `// of equal radius when the radius` `// of the circumscribed circle is given` `#include <bits/stdc++.h>` `using` `namespace` `std;` `void` `threetangcircle(` `int` `R)` `{` ` ` `cout << ` `"The radii of the tangent circles is "` ` ` `<< 0.4645 * R << endl;` `}` `// Driver code` `int` `main()` `{` ` ` `int` `R = 4;` ` ` `threetangcircle(R);` ` ` `return` `0;` `}` |

```
// Java program to find the radii
// of the three tangent circles
// of equal radius when the radius
// of the circumscribed circle is given
import java.io.*;
class GFG
{
static void threetangcircle(int R)
{
System.out.print("The radii of the tangent circles is "
+ 0.4645 * R);
}
// Driver code
public static void main (String[] args)
{
int R = 4;
threetangcircle(R);
}
}
// This code is contributed by anuj_67..
```

## Python3

`# Python3 program to find the radii` `# of the three tangent circles` `# of equal radius when the radius` `# of the circumscribed circle is given` `def` `threetangcircle(R):` ` ` `print` `(` `"The radii of the tangent"` `,` ` ` `"circles is "` `, end ` `=` `"");` ` ` `print` `(` `0.4645` `*` `R);` `# Driver code` `R ` `=` `4` `;` `threetangcircle(R);` `# This code is contributed` `# by Princi Singh` |

## C#

`// C# program to find the radii` `// of the three tangent circles` `// of equal radius when the radius` `// of the circumscribed circle is given` `using` `System;` `class` `GFG` `{` `static` `void` `threetangcircle(` `int` `R)` `{` ` ` `Console.WriteLine(` `"The radii of the tangent circles is "` ` ` `+ 0.4645 * R);` `}` `// Driver code` `public` `static` `void` `Main ()` `{` ` ` `int` `R = 4;` ` ` `threetangcircle(R);` `}` `}` `// This code is contributed by anuj_67..` |

```
<?php
// PHP program to find the radii
// of the three tangent circles
// of equal radius when the radius
// of the circumscribed circle is given
function threetangcircle($R)
{
echo "The radii of the tangent circles is ",
( 0.4645 * $R );
}
// Driver code
$R = 4;
threetangcircle($R);
// This code is contributed by ihritik
?>
```

## Javascript

`<script>` `// javascript program to find the radii` `// of the three tangent circles` `// of equal radius when the radius` `// of the circumscribed circle is given` `function` `threetangcircle(R)` `{` ` ` `document.write(` `"The radii of the tangent circles is "` ` ` `+ 0.4645 * R);` `}` `// Driver code` `var` `R = 4;` `threetangcircle(R);` `// This code contributed by shikhasingrajput` `</script>` |

**Output:**

The radii of the tangent circles is 1.858

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