# Length of the direct common tangent between two externally touching circles

Given two circles, of given radii, that touch each other externally. The task is to find the length of the direct common tangent between the circles.

**Examples:**

Input:r1 = 5, r2 = 9Output:13.4164Input:r1 = 11, r2 = 13Output:23.9165

**Approach**

- Let the radii be
**r1**&**r2**respectively. - Draw a line
**OR**parallel to**PQ** **angle OPQ = 90 deg**

angle O’QP = 90 deg

{ line joining the centre of the circle to the point of contact makes an angle of 90 degrees with the tangent }**angle OPQ + angle O’QP = 180**

OP || QR- Since opposite sides are parallel and interior angles are 90, therefore
**OPQR**is a rectangle. - So
**OP = QR = r1**and**PQ = OR = r1+r2** - In triangle
**OO’R****angle ORO’ = 90**

By**Pythagoras theorem****OR^2 + O’R^2 = OO’^2**

OO’^2 = (r1+r2)^2 + (r1-r2)^2 - So,
**OO’ = 2√(r1*r2)**

Below is the implementation of the above approach:

## C++

`// C++ program to find the length of the direct ` `// common tangent between two circles ` `// which externally touch each other ` ` ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Function to find the length ` `// of the direct common tangent ` `void` `lengtang(` `double` `r1, ` `double` `r2) ` `{ ` ` ` `cout << ` `"The length of the "` ` ` `<< ` `"direct common tangent is "` ` ` `<< 2 * ` `sqrt` `(r1 * r2) << endl; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `double` `r1 = 5, r2 = 9; ` ` ` `lengtang(r1, r2); ` ` ` `return` `0; ` `} ` |

*chevron_right*

*filter_none*

## Java

`// Java program to find the length of the direct ` `// common tangent between two circles ` `// which externally touch each other ` `class` `GFG ` `{ ` ` ` ` ` `// Function to find the length ` ` ` `// of the direct common tangent ` ` ` `static` `void` `lengtang(` `double` `r1, ` `double` `r2) ` ` ` `{ ` ` ` `System.out.println(` `"The length of the "` ` ` `+ ` `"direct common tangent is "` ` ` `+ (` `2` `* Math.sqrt(r1 * r2))); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main(String[] args) ` ` ` `{ ` ` ` `double` `r1 = ` `5` `, r2 = ` `9` `; ` ` ` `lengtang(r1, r2); ` ` ` `} ` `} ` ` ` `// This code contributed by Rajput-Ji ` |

*chevron_right*

*filter_none*

## Python3

`# Python3 program to find the length ` `# of the direct common tangent ` `# between two circles which ` `# externally touch each other ` ` ` `# Function to find the length ` `# of the direct common tangent ` `def` `lengtang(r1, r2): ` ` ` `print` `(` `"The length of the direct"` `, ` ` ` `"common tangent is"` `, ` ` ` `2` `*` `(r1 ` `*` `r2)` `*` `*` `(` `1` `/` `2` `)); ` ` ` `# Driver code ` `r1 ` `=` `5` `; r2 ` `=` `9` `; ` `lengtang(r1, r2); ` ` ` `# This code contributed ` `# by PrinciRaj1992 ` |

*chevron_right*

*filter_none*

## C#

`// C# program to find the length of the direct ` `// common tangent between two circles ` `// which externally touch each other ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` `// Function to find the length ` ` ` `// of the direct common tangent ` ` ` `static` `void` `lengtang(` `double` `r1, ` `double` `r2) ` ` ` `{ ` ` ` `Console.WriteLine(` `"The length of the "` ` ` `+ ` `"direct common tangent is "` ` ` `+ (2 * Math.Sqrt(r1 * r2))); ` ` ` `} ` ` ` ` ` `// Driver code ` ` ` `static` `public` `void` `Main () ` ` ` `{ ` ` ` `double` `r1 = 5, r2 = 9; ` ` ` `lengtang(r1, r2); ` ` ` `} ` `} ` ` ` `// This code contributed by ajit. ` |

*chevron_right*

*filter_none*

## PHP

`<?php ` `// PHP program to find the length of the direct ` `// common tangent between two circles ` `// which externally touch each other ` ` ` `// Function to find the length ` `// of the direct common tangent ` `function` `lengtang(` `$r1` `, ` `$r2` `) ` `{ ` ` ` `echo` `"The length of the "` ` ` `, ` `"direct common tangent is "` ` ` `, 2 * sqrt(` `$r1` `* ` `$r2` `) ; ` `} ` ` ` `// Driver code ` `$r1` `= 5; ` `$r2` `= 9; ` `lengtang(` `$r1` `, ` `$r2` `); ` ` ` `// This code is contributed by AnkitRai01 ` ` ` `?> ` |

*chevron_right*

*filter_none*

**Output:**

The length of the direct common tangent is 13.4164

## Recommended Posts:

- Length of direct common tangent between the two non-intersecting Circles
- Length of direct common tangent between two intersecting Circles
- Length of the transverse common tangent between the two non intersecting circles
- Ratio of the distance between the centers of the circles and the point of intersection of two direct common tangents to the circles
- Length of rope tied around three equal circles touching each other
- Distance between centers of two intersecting circles if the radii and common chord length is given
- Ratio of the distance between the centers of the circles and the point of intersection of two transverse common tangents to the circles
- Radii of the three tangent circles of equal radius which are inscribed within a circle of given radius
- Number of common tangents between two circles if their centers and radius is given
- Length of the perpendicular bisector of the line joining the centers of two circles
- Maximum length subsequence such that adjacent elements in the subsequence have a common factor
- Find Tangent at a given point on the curve
- Print first n Fibonacci Numbers using direct formula
- Number of triangles formed by joining vertices of n-sided polygon with two common sides and no common sides
- Check if two given Circles are Orthogonal or not

If you like GeeksforGeeks and would like to contribute, you can also write an article using contribute.geeksforgeeks.org or mail your article to contribute@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

Please Improve this article if you find anything incorrect by clicking on the "Improve Article" button below.