Program to Find the Incenter of a Triangle

Given the vertices of a triangle and length of its sides. A circle is inscribed in a triangle. The task is to find the incenter of a triangle.

**Examples:**

Input:A(2, 2), B(1, 1), C(3, 1) and AB = 2, BC = 1, AC = 1Output:(2, 1.5)Input:A(3, 3), B(1, 2), C(2, 2) and AB = 3, BC = 2, AC = 2Output:(2.5, 2.83)

**Approach:**

- The centre of the circle that touches the sides of a triangle is called its incenter.
- Suppose the vertices of the triangle are A(x1, y1), B(x2, y2) and C(x3, y3).
- Let the side AB = a, BC = b, AC = c then the coordinates of the in-center is given by the formula:

Below is the implementation of the above approach:

## C++

`// C++ program to find the ` `// incenter of a triangle ` `#include <bits/stdc++.h> ` `using` `namespace` `std; ` ` ` `// Driver code ` `int` `main() ` `{ ` ` ` `// coordinate of the vertices ` ` ` `float` `x1 = 2, x2 = 1, x3 = 3; ` ` ` `float` `y1 = 2, y2 = 1, y3 = 1; ` ` ` `float` `a = 2, b = 1, c = 1; ` ` ` ` ` `// Formula to calculate in-center ` ` ` `float` `x = (a * x1 + b * ` ` ` `x2 + c * x3) / (a + b + c); ` ` ` `float` `y = (a * y1 + b * ` ` ` `y2 + c * y3) / (a + b + c); ` ` ` ` ` `// System.out.print(setprecision(3)); ` ` ` `cout << ` `"Incenter = "` ` ` `<< ` `"("` `<< x << ` `", "` `<< y << ` `")"` `; ` ` ` `return` `0; ` `} ` ` ` `// This code is contributed by 29AjayKumar ` |

## Java

`// Java program to find the ` `// incenter of a triangle ` ` ` `import` `java.util.*; ` `import` `java.lang.*; ` ` ` `class` `GFG { ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `main(String args[]) ` ` ` `{ ` ` ` `// coordinate of the vertices ` ` ` `float` `x1 = ` `2` `, x2 = ` `1` `, x3 = ` `3` `; ` ` ` `float` `y1 = ` `2` `, y2 = ` `1` `, y3 = ` `1` `; ` ` ` `float` `a = ` `2` `, b = ` `1` `, c = ` `1` `; ` ` ` ` ` `// Formula to calculate in-center ` ` ` `float` `x ` ` ` `= (a * x1 + b * x2 + c * x3) / (a + b + c); ` ` ` `float` `y ` ` ` `= (a * y1 + b * y2 + c * y3) / (a + b + c); ` ` ` ` ` `// System.out.print(setprecision(3)); ` ` ` `System.out.println(` `"Incenter= "` ` ` `+ ` `"("` `+ x + ` `", "` `+ y + ` `")"` `); ` ` ` `} ` `} ` |

## Python3

`# Python3 program to find the ` `# incenter of a triangle ` ` ` `# Driver code ` ` ` `# coordinate of the vertices ` `x1 ` `=` `2` `; x2 ` `=` `1` `; x3 ` `=` `3` `; ` `y1 ` `=` `2` `; y2 ` `=` `1` `; y3 ` `=` `1` `; ` `a ` `=` `2` `; b ` `=` `1` `; c ` `=` `1` `; ` ` ` `# Formula to calculate in-center ` `x ` `=` `(a ` `*` `x1 ` `+` `b ` `*` `x2 ` `+` `c ` `*` `x3) ` `/` `(a ` `+` `b ` `+` `c); ` `y ` `=` `(a ` `*` `y1 ` `+` `b ` `*` `y2 ` `+` `c ` `*` `y3) ` `/` `(a ` `+` `b ` `+` `c); ` ` ` `# System.out.print(setprecision(3)); ` `print` `(` `"Incenter = ("` `, x, ` `","` `, y, ` `")"` `); ` ` ` `# This code is contributed ` `# by Akanksha Rai ` |

## C#

`// C# program to find the ` `// incenter of a triangle ` ` ` `using` `System; ` ` ` `class` `GFG ` `{ ` ` ` ` ` `// Driver code ` ` ` `public` `static` `void` `Main() ` ` ` `{ ` ` ` `// coordinate of the vertices ` ` ` `float` `x1 = 2, x2 = 1, x3 = 3; ` ` ` `float` `y1 = 2, y2 = 1, y3 = 1; ` ` ` `float` `a = 2, b = 1, c = 1; ` ` ` ` ` `// Formula to calculate in-center ` ` ` `float` `x ` ` ` `= (a * x1 + b * x2 + c * x3) / (a + b + c); ` ` ` `float` `y ` ` ` `= (a * y1 + b * y2 + c * y3) / (a + b + c); ` ` ` ` ` `// System.out.print(setprecision(3)); ` ` ` `Console.WriteLine(` `"Incenter= "` ` ` `+ ` `"("` `+ x + ` `", "` `+ y + ` `")"` `); ` ` ` `} ` `} ` ` ` `// This code is contributed by vt_m. ` |

**Output:**

Incenter= (2.0, 1.5)

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