# 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; ` `} ` |

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## Java

`// 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.. ` |

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## 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 ` |

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## 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.. ` |

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## PHP

`<?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 ` `?> ` |

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**Output:**

The radii of the tangent circles is 1.858

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