Area of Circumcircle and Incircle of a Right Kite (original) (raw)

Last Updated : 23 Jul, 2025

Given two positive integers A and B representing the sides of the right kite, the task is to find the area of the circumcircle and incircle of a right kite.

A right kite is a kite that can be inscribed in a circle with two opposite angles are at right angles. The line of symmetry of the kite is also the diameter of the circumcircle of the kite. It divides the kite into two congruent right-angled triangles having sides as A and B of a right kite.

Examples:

Input: A = 3, B = 4
Output: Area of circumcircle of Right Kite is 19.625, Area of incircle of Right Kite is 3.14

Input: A = 10, B = 5
Output: Area of circumcircle of Right Kite is 98.125, Area of incircle of Right Kite is 28.26

Approach: There are some observations to solve this problem. Follow the steps below to solve this problem:

Here, a = AB = AD and b = BC = CD
In the kite ABCD with opposite angles B and D as 90°, thus the opposite angles can be calculated as tan (A/2) = b/a and tan(C/2) = a/b
Let p as the length of diagonal AC and q as the length of diagonal BD.
Diagonal AC can be easily calculated using the Pythagoras Theorem. Hence p = (a2 + b2)½
Since the diagonal is equal to the diameter of the circumcircle of the kite, the radius of the circumcircle is calculated as R = (a2 + b2)½/2
Thus, the area of the circumcircle will be pi * R* R
Also**,** all kites are tangential quadrilaterals, therefore the radius of the incircle can be calculated by r = Area of kite/Semiperimeter of the kite i.e r = a*b/(a+b).
Thus, the area of the incircle will be pi*r*r.

Below is the implementation of the above approach:

C++ `

// C++ program for the above approach

#include <bits/stdc++.h> using namespace std; #define pi 3.14

// Function to calculate the area of // circumcircle of right kite double AreaOfCircumcircle(int a, int b) { // Find the radius double radius = sqrt(a * a + b * b) / 2; return pi * radius * radius; }

// Function to calculate the area of // incircle of right kite double AreaOfIncircle(int a, int b) { // Find the radius double radius = (a * b) / (a + b);

return pi * radius * radius;

}

// Driver Code int main() { // Given Input int a, b; a = 10; b = 5;

// Function Call
double circumarea = AreaOfCircumcircle(
    a, b);
cout << "Area of circumcircle of Right Kite is"
     << " " << circumarea << endl;

// Function Call
double inarea = AreaOfIncircle(
    a, b);
cout << "Area of incircle of Right Kite is"
     << " " << inarea << endl;

return 0;

}

Java

// Java program for the above approach public class GFG { static double pi = 3.14;

// Function to calculate the area of
// circumcircle of right kite
static double AreaOfCircumcircle(int a, int b)
{
    // Find the radius
    double radius = Math.sqrt(a * a + b * b) / 2;
    return pi * radius * radius;
}

// Function to calculate the area of
// incircle of right kite
static double AreaOfIncircle(int a, int b)
{
    // Find the radius
    double radius = (a * b) / (a + b);

    return pi * radius * radius;
}

// Driver code
public static void main(String[] args)
{
  
    // Given Input
    int a, b;
    a = 10;
    b = 5;

    // Function Call
    double circumarea = AreaOfCircumcircle(a, b);
    System.out.printf(
        "Area of circumcircle of Right Kite is %.3f\n",
        circumarea);

    // Function Call
    double inarea = AreaOfIncircle(a, b);
    System.out.printf(
        "Area of incircle of Right Kite is %.2f\n",
        inarea);
}

}

// This code is contributed by abhinavjain194

Python3

Python program for the above approach

Function to calculate the area of

circumcircle of right kite

import math pi = 3.14

def AreaOfCircumcircle(a, b):

# Find the radius
radius = math.sqrt(a * a + b * b)/ 2
return pi * radius * radius

Function to calculate the area of

incircle of right kite

def AreaOfIncircle( a, b):

# Find the radius
radius = (a * b) // (a + b)
return pi * (radius**2)

Driver Code

Given Input

a = 10 b = 5

Function Call

circumarea = AreaOfCircumcircle(a, b) print("Area of circumcircle of Right Kite is" ," " , format(circumarea,".3f"))

Function Call

inarea = AreaOfIncircle(a, b) print("Area of incircle of Right Kite is" ," " , format(inarea,".2f"))

this code is contributed by shivanisinghss2110

C#

// C# program for the above approach using System;

class GFG{

static double pi = 3.14;

// Function to calculate the area of // circumcircle of right kite static double AreaOfCircumcircle(int a, int b) {

// Find the radius
double radius = Math.Sqrt(a * a + b * b) / 2;
return pi * radius * radius;

}

// Function to calculate the area of // incircle of right kite static double AreaOfIncircle(int a, int b) {

// Find the radius
double radius = (a * b) / (a + b);

return pi * radius * radius;

}

// Driver code public static void Main() {

// Given Input
int a, b;
a = 10;
b = 5;

// Function Call
double circumarea = AreaOfCircumcircle(a, b);
Console.WriteLine(
    "Area of circumcircle of Right Kite is " + 
    circumarea);

// Function Call
double inarea = AreaOfIncircle(a, b);
Console.WriteLine(
    "Area of incircle of Right Kite is " + inarea);

} }

// This code is contributed by subhammahato348

JavaScript

Output

Area of circumcircle of Right Kite is 98.125 Area of incircle of Right Kite is 28.26

Time Complexity: O(logn) since using inbuilt sqrt function
Auxiliary Space: O(1)