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++
// C++ program to find the// incenter of a triangle#include <bits/stdc++.h>using namespace std;// Driver codeint 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 triangleimport 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 verticesx1 = 2; x2 = 1; x3 = 3;y1 = 2; y2 = 1; y3 = 1;a = 2; b = 1; c = 1;# Formula to calculate in-centerx = (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 triangleusing 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. |
Javascript
<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> |
Output
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.
