# 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 = 1
Output: (2, 1.5)

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

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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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Improved By : vt_m, 29AjayKumar, Akanksha_Rai