# Distance between Incenter and Circumcenter of a triangle using Inradius and Circumradius

Given two integers **r **and **R** representing the length of** Inradius** and **Circumradius** respectively, the task is to calculate the distance **d** between Incenter and Circumcenter.

**Inradius **The inradius( r ) of a regular triangle( ABC ) is the radius of the incircle (having center as l), which is the largest circle that will fit inside the triangle. **Circumradius: **The circumradius( R ) of a triangle is the radius of the circumscribed circle (having center as O) of that triangle.

**Examples:**

Input:r = 2, R = 5Output:2.24

Input:r = 5, R = 12Output:4.9

**Approach:**

The problem can be solved using **Euler’s Theorem** in geometry, which states that the distance between the incenter and circumcenter of a triangle can be calculated by the equation:

Below is the implementation of the above approach:

## C++14

`// C++14 program for the above approach` `#include <bits/stdc++.h> ` `using` `namespace` `std;` ` ` `// Function returns the required distance` `double` `distance(` `int` `r, ` `int` `R) ` `{ ` ` ` `double` `d = ` `sqrt` `(` `pow` `(R, 2) - ` ` ` `(2 * r * R)); ` ` ` ` ` `return` `d; ` `} ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` ` ` `// Length of Inradius ` ` ` `int` `r = 2; ` ` ` ` ` `// Length of Circumradius ` ` ` `int` `R = 5; ` ` ` ` ` `cout << (round(distance(r, R) * 100.0) / 100.0); ` `} ` ` ` `// This code is contributed by sanjoy_62` |

## Java

`// Java program for the above approach ` `import` `java.util.*;` ` ` `class` `GFG{` ` ` `// Function returns the required distance` `static` `double` `distance(` `int` `r,` `int` `R)` `{` ` ` `double` `d = Math.sqrt(Math.pow(R, ` `2` `) -` ` ` `(` `2` `* r * R));` ` ` ` ` `return` `d;` `}` ` ` `// Driver code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Length of Inradius` ` ` `int` `r = ` `2` `;` ` ` ` ` `// Length of Circumradius` ` ` `int` `R = ` `5` `;` ` ` ` ` `System.out.println(Math.round(` ` ` `distance(r, R) * ` `100.0` `) / ` `100.0` `);` `}` `}` ` ` `// This code is contributed by offbeat` |

## Python3

`# Python3 program for the above approach` `import` `math` ` ` `# Function returns the required distance` `def` `distance(r,R):` ` ` ` ` `d ` `=` `math.sqrt( (R` `*` `*` `2` `) ` `-` `(` `2` `*` `r ` `*` `R))` ` ` ` ` `return` `d` ` ` `# Driver Code` ` ` `# Length of Inradius` `r ` `=` `2` ` ` `# Length of Circumradius` `R ` `=` `5` ` ` `print` `(` `round` `(distance(r,R),` `2` `))` |

## C#

`// C# program for the above approach ` `using` `System;` ` ` `class` `GFG{` ` ` `// Function returns the required distance` `static` `double` `distance(` `int` `r, ` `int` `R)` `{` ` ` `double` `d = Math.Sqrt(Math.Pow(R, 2) -` ` ` `(2 * r * R));` ` ` ` ` `return` `d;` `}` ` ` `// Driver code` `public` `static` `void` `Main(` `string` `[] args)` `{` ` ` ` ` `// Length of Inradius` ` ` `int` `r = 2;` ` ` ` ` `// Length of Circumradius` ` ` `int` `R = 5;` ` ` ` ` `Console.Write(Math.Round(` ` ` `distance(r, R) * 100.0) / 100.0);` `}` `}` ` ` `// This code is contributed by rutvik_56` |

## Javascript

`<script>` ` ` `// Javascript program for` `// the above approach` ` ` `// Function returns the required distance` `function` `distance(r, R)` `{` ` ` `let d = Math.sqrt(Math.pow(R, 2) -` ` ` `(2 * r * R));` ` ` ` ` `return` `d;` `}` ` ` `// Driver code` ` ` ` ` `// Length of Inradius` ` ` `let r = 2;` ` ` ` ` `// Length of Circumradius` ` ` `let R = 5;` ` ` ` ` `document.write(Math.round(` ` ` `distance(r, R) * 100.0) / 100.0);` ` ` ` ` `// This code is contributed by susmitakundugoaldanga.` `</script>` |

**Output:**

2.24

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