Area of Circumcircle of a Right Angled Triangle

Last Updated : 25 Mar, 2021

Given an integer C which is the length of the hypotenuse of a right angled triangle of a circumcircle passing through the centre of the circumcircle. The task is to find the area of the circumcircle.

Examples:

Input: C = 8
Output: 50.26
Input: C = 10
Output: 78.53

Approach: Since the hypotenuse C passes through the center of the circle, the radius of the circle will be C / 2.
And we know that the area of a circle is PI * r² where PI = 22 / 7 and r is the radius of the circle.
Hence the area of the circumcircle will be PI * (C / 2)² i.e. PI * C² / 4.
Below is the implementation of the above approach:

C++

// C++ program to find the area of Cicumscribed
// circle of right angled triangle
#include <bits/stdc++.h>
#define PI 3.14159265
using namespace std;
 
// Function to find area of
// circumscribed circle
float area_circumscribed(float c)
{
    return (c * c * (PI / 4));
}
 
// Driver code
int main()
{
    float c = 8;
    cout << area_circumscribed(c);
    return 0;
}
 
// This code is contributed by Shivi_Aggarwal

C

// C program to find the area of Cicumscribed
// circle of right angled triangle
#include <stdio.h>
#define PI 3.14159265
 
// Function to find area of
// circumscribed circle
float area_circumscribed(float c)
{
    return (c * c * (PI / 4));
}
 
// Driver code
int main()
{
    float c = 8;
    printf("%f",
           area_circumscribed(c));
    return 0;
}

Java

// Java code to find the area of circumscribed
// circle of right angled triangle
import java.lang.*;
 
class GFG {
 
    static double PI = 3.14159265;
 
    // Function to find the area of
    // circumscribed circle
    public static double area_cicumscribed(double c)
    {
        return (c * c * (PI / 4));
    }
 
    // Driver code
    public static void main(String[] args)
    {
        double c = 8.0;
        System.out.println(area_cicumscribed(c));
    }
}

Python3

# Python3 code to find the area of circumscribed
# circle of right angled triangle
PI = 3.14159265
     
# Function to find the area of
# circumscribed circle
def area_cicumscribed(c):
    return (c * c * (PI / 4))
     
# Driver code
c = 8.0
print(area_cicumscribed(c))

C#

// C# code to find the area of
// circumscribed circle
// of right angled triangle
using System;
 
class GFG {
    static double PI = 3.14159265;
 
    // Function to find the area of
    // circumscribed circle
    public static double area_cicumscribed(double c)
    {
        return (c * c * (PI / 4));
    }
 
    // Driver code
    public static void Main()
    {
        double c = 8.0;
        Console.Write(area_cicumscribed(c));
    }
}

PHP

<?php
// PHP program to find the
// area of Cicumscribed
// circle of right angled triangle
$PI = 3.14159265;
 
// Function to find area of
// circumscribed circle
function area_circumscribed($c)
{
    global $PI;
    return ($c * $c * ($PI / 4));
}
 
// Driver code
$c = 8;
echo(area_circumscribed($c));
?>

Javascript

<script>
// javascript code to find the area of circumscribed
// circle of right angled triangle
 
    let PI = 3.14159265;
 
    // Function to find the area of
    // circumscribed circle
    function area_cicumscribed(c) {
        return (c * c * (PI / 4));
    }
 
    // Driver code
    var c = 8.0;
    document.write(area_cicumscribed(c).toFixed(6));
 
// This code is contributed by Rajput-Ji
</script>

Output:

50.265484

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