右风筝的外圆和内圆面积

给定两个正整数A和B代表右风筝的边，任务是找到右风筝的外接圆和内圆的面积。

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.

例子：

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

方法：有一些观察可以解决这个问题。请按照以下步骤解决此问题：

• 这里， a = AB = AD和b = BC = CD
• 在风筝ABCD 中， B和D 的对角为90° ，因此对角可以计算为tan (A/2) = b/a和tan(C/2) = a/b
• 设p为对角线AC的长度， q为对角线BD的长度。
• 使用毕达哥拉斯定理可以轻松计算对角线AC 。因此p = (a ² + b ² ) ^½
• 由于对角线等于风筝外接圆的直径，外接圆的半径计算为R = (a ² + b ² ) ^½ /2
• 因此，外接圆的面积将是pi * R* R
• 此外，所有风筝都是切线四边形，因此内圆的半径可以通过r = 风筝面积/风筝的半周长来计算，即r = a*b/(a+b)。
• 因此，内圆的面积将为pi*r*r。

下面是上述方法的实现：

C++

// C++ program for the above approach
 
#include 
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

  
        // 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
 

输出

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

时间复杂度：O(1)
辅助空间：O(1)

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