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; ` `} ` |

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## 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 ` |

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## 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 ` |

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## 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. ` |

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## 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 ` ` ` `?> ` |

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**Output:**

The length of the direct common tangent is 13.4164

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