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) 
Output: (2, 1.5)

Input: A(3, 3), B(1, 2), C(2, 2) 
Output: (2.5, 2.83)

Approach: 
 

• The center 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++ 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 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 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# 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.

<script>
      // JavaScript program to find the
      // incenter of a triangle
      // Driver code
      // coordinate of the vertices
      var x1 = 2,
        x2 = 1,
        x3 = 3;
      var y1 = 2,
        y2 = 1,
        y3 = 1;
      var a = 2,
        b = 1,
        c = 1;

      // Formula to calculate in-center
      var x = (a * x1 + b * x2 + c * x3) / (a + b + c);
      var y = (a * y1 + b * y2 + c * y3) / (a + b + c);

      document.write(
        "Incenter = " + "(" + x.toFixed(1) + ", " + y.toFixed(1) + ")"
      );
    </script>

Incenter = (2, 1.5)

Time Complexity: O(1), the code will run in a constant time.
Auxiliary Space: O(1), no extra space is required, so it is a constant.