Program to find the Radius of the incircle of the triangle

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Given a circle which is the incircle of a triangle whose sides are a, b< and c, the task is to find the radius of this incircle.

Examples:

Input: a = 2, b = 2, c = 3
Output: 0.566947

Input: a = 3, b = 4, c = 5
Output: 1

Approach:

Radius of the incircle = area of the triangle / half of perimeter of the triangle
where:
Area of the triangle = √(p*(p-a)*(p-b)*(p-c)
perimeter of the triangle = (a + b + c)

Below is the implementation of the above approach:

C++

// C++ Program to find the radius
// of the incircle of the given triangle
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to find the radius
// of the incircle
float findRadiusOfIncircle(float a, float b, float c)
{
 
    // the sides cannot be negative
    if (a < 0 || b < 0 || c < 0)
        return -1;
 
    // semi-perimeter of the circle
    float p = (a + b + c) / 2;
 
    // area of the triangle
    float area = sqrt(p * (p - a) * (p - b) * (p - c));
 
    // Radius of the incircle
    float radius = area / p;
 
    // Return the radius
    return radius;
}
 
// Driver code
int main()
{
 
    // Get the sides of the triangle
    float a = 2, b = 2, c = 3;
 
    // Find the radius of the incircle
    cout << findRadiusOfIncircle(a, b, c)
         << endl;
 
    return 0;
}

Java

// Java Program to find the radius
// of the incircle of the given triangle
import java.io.*;
 
class GFG {
   
// Function to find the radius
// of the incircle
static float findRadiusOfIncircle(float a, float b, float c)
{
 
    // the sides cannot be negative
    if (a < 0 || b < 0 || c < 0)
        return -1;
 
    // semi-perimeter of the circle
    float p = (a + b + c) / 2;
 
    // area of the triangle
    float area = (float)Math.sqrt(p * (p - a) * (p - b) * (p - c));
 
    // Radius of the incircle
    float radius = area / p;
 
    // Return the radius
    return radius;
}
 
// Driver code
 
    public static void main (String[] args) {
         
    // Get the sides of the triangle
    float a = 2, b = 2, c = 3;
 
    // Find the radius of the incircle
    System.out.println( findRadiusOfIncircle(a, b, c));
         
    }
}
 // This code is contributed by ajit

Python3

# Python Program to find the radius 
# of the incircle of the given triangle 
 
# from math lib. import everything
from math import *
 
# Function to find the radius 
# of the incircle 
def findRadiusOfIncircle(a, b, c) :
 
    # the sides cannot be negative 
    if (a < 0 or b < 0 or c < 0) :
        return -1
 
    # semi-perimeter of the circle 
    p = (a + b + c) / 2
 
    # area of the triangle 
    area = sqrt(p * (p - a) *
               (p - b) * (p - c)) 
 
    # Radius of the incircle 
    radius = area / p 
 
    # Return the radius 
    return radius 
 
# Driver code     
if __name__ == "__main__" :
 
    # Get the sides of the triangle 
    a, b, c = 2, 2, 3
 
    # Find the radius of the incircle 
    print(round(findRadiusOfIncircle(a, b, c), 6)) 
 
# This code is contributed by ANKITRAI1

C#

// C# Program to find the radius
// of the incircle of the given triangle
using System;
 
class GFG 
{
 
// Function to find the radius
// of the incircle
public static float findRadiusOfIncircle(float a,
                                         float b, 
                                         float c)
{
 
    // the sides cannot be negative
    if (a < 0 || b < 0 || c < 0)
        return -1;
     
    // semi-perimeter of the circle
    float p = (a + b + c) / 2;
     
    // area of the triangle
    float area = (float)Math.Sqrt(p * (p - a) * 
                          (p - b) * (p - c));
     
    // Radius of the incircle
    float radius = area / p;
     
    // Return the radius
    return (float)(radius);
}
 
// Driver code
public static void Main()
{
 
    // Get the sides of the triangle
    float a = 2, b = 2, c = 3;
 
    // Find the radius of the incircle
    Console.WriteLine(findRadiusOfIncircle(a, b, c));
}
}
 
// This code is contributed
// by Shivi_Aggarwal

PHP

<?php
// PHP Program to find the radius
// of the incircle of the given triangle
 
// Function to find the radius
// of the incircle
function findRadiusOfIncircle($a, $b, $c)
{
 
    // the sides cannot be negative
    if ($a < 0 || $b < 0 || $c < 0)
        return -1;
 
    // semi-perimeter of the circle
    $p = ($a + $b + $c) / 2;
 
    // area of the triangle
    $area = sqrt($p * ($p - $a) *
                ($p - $b) * ($p - $c));
 
    // Radius of the incircle
    $radius = $area / $p;
 
    // Return the radius
    return $radius;
}
 
// Driver code
 
// Get the sides of the triangle
$a = 2; $b = 2; $c = 3;
 
// Find the radius of the incircle
echo findRadiusOfIncircle($a, $b, $c) . "\n";
 
// This code is contributed 
// by Akanksha Rai(Abby_akku)

Javascript

<script>
 
// javascript Program to find the radius
// of the incircle of the given triangle
 
   
// Function to find the radius
// of the incircle
function findRadiusOfIncircle(a , b , c)
{
 
    // the sides cannot be negative
    if (a < 0 || b < 0 || c < 0)
        return -1;
 
    // semi-perimeter of the circle
    var p = (a + b + c) / 2;
 
    // area of the triangle
    var area = Math.sqrt(p * (p - a) * (p - b) * (p - c));
 
    // Radius of the incircle
    var radius = area / p;
 
    // Return the radius
    return radius;
}
 
// Driver code
 
// Get the sides of the triangle
var a = 2, b = 2, c = 3;
 
// Find the radius of the incircle
document.write( findRadiusOfIncircle(a, b, c).toFixed(6));
 
// This code contributed by shikhasingrajput 
 
</script>

Output:

0.566947

Time complexity: O(log(n)) because using inbuilt sqrt function

Auxiliary Space: O(1), since no extra space has been taken.

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