Area of Circumcircle and Incircle of a Right Kite
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 3.14Input: 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
<script> // JavaScript Program for the above approach var pi = 3.14 // Function to calculate the area of // circumcircle of right kite function AreaOfCircumcircle(a, b) { // Find the radius let radius = Math.sqrt(a * a + b * b) / 2; return pi * radius * radius; } // Function to calculate the area of // incircle of right kite function AreaOfIncircle(a, b) { // Find the radius let radius = (a * b) / (a + b); return pi * radius * radius; } // Driver Code // Given Input let a, b; a = 10; b = 5; // Function Call let circumarea = AreaOfCircumcircle(a, b); document.write( "Area of circumcircle of Right Kite is " + (circumarea.toFixed(3)) + "<br>" ); // Function Call let inarea = AreaOfIncircle( a, b); document.write( "Area of incircle of Right Kite is " + (inarea.toFixed(3)) + "<br>" ); // This code is contributed by Potta Lokesh </script> |
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)