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)



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++

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// 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

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Java














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// 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 + ")"); 


    } 


} 



















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Python3














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# 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 



















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C#














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// 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. 



















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Output:


Incenter= (2.0, 1.5)








    

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Improved By :  vt_m, 29AjayKumar, Akanksha_Rai