# 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 = 4
Output: 1.858

Input: R = 11
Output: 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

Below is the implementation of the above approach:

## 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 ` `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

 `// 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..`

## Javascript

 ``

## PHP

 ``

Output

```The radii of the tangent circles is 1.858
```

Time Complexity: O(1)
Auxiliary Space: O(1)

Feeling lost in the world of random DSA topics, wasting time without progress? It's time for a change! Join our DSA course, where we'll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 geeks!

Previous
Next