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Area of Circumcircle of a Right Angled Triangle
  • Last Updated : 30 Jan, 2019

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++

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// 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

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C

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// 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;
}

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Java

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// 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));
    }
}

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Python3

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# 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))

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C#

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// 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));
    }
}

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PHP

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<?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));
?>

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Output:

50.265484

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