Length of Diagonals of a Cyclic Quadrilateral using the length of Sides.

0 0 3 minutes read

Given integers A, B, C, and D, denoting the length of sides of a Cyclic Quadrilateral, the task is to find the length of diagonals of a cyclic quadrilateral.

Examples:

Input: A = 10, B = 15, C = 20, D = 25
Output: 22.06 26.07

Input: A = 10, B = 30, C =50, D = 20
Output: 37.93 29.0

Approach: The length of diagonals can be calculated using the following equations:

$Diagonal (p)=\sqrt{\frac{(ac+bd)(ad+bc)}{ab+cd}}$ [Tex]Diagonal (q)=\sqrt{\frac{(ac+bd)(ab+cd)}{ad+bc}} [/Tex]

Below is the implementation of the above approach:

C++

// C++ Program to implement
// the above approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate the length of
// diagonals of a cyclic quadrilateral
vector<float> Diagonals(int a, int b, 
                        int c, int d)
{
    vector<float> ans;
    ans.push_back(sqrt(((a * c) + (b * d)) * 
                       ((a * d) + (b * c)) / 
                       ((a * b) + (c * d))));
    ans.push_back(sqrt(((a * c) + (b * d)) * 
                       ((a * b) + (c * d)) / 
                       ((a * d) + (b * c))));
    return ans;
}
 
// Driver Code
int main()
{
    int A = 10;
    int B = 15;
    int C = 20;
    int D = 25;
 
    // Function Call
    vector<float> ans = Diagonals(A, B, C, D);
 
    // Print the final answer
    printf("%.2f %.2f", 
           (ans[0]) + .01, 
            ans[1] + .01);
}
 
// This code is contributed by Amit Katiyar

Java

// Java Program to implement
// the above approach
import java.util.*;
class GFG{
 
// Function to calculate the length of
// diagonals of a cyclic quadrilateral
static Vector<Float> Diagonals(int a, int b, 
                               int c, int d)
{
    Vector<Float> ans = new Vector<Float>();
    ans.add((float) Math.sqrt(((a * c) + (b * d)) * 
                              ((a * d) + (b * c)) / 
                              ((a * b) + (c * d))));
    ans.add((float) Math.sqrt(((a * c) + (b * d)) * 
                              ((a * b) + (c * d)) / 
                              ((a * d) + (b * c))));
    return ans;
}
 
// Driver Code
public static void main(String[] args)
{
    int A = 10;
    int B = 15;
    int C = 20;
    int D = 25;
 
    // Function Call
    Vector<Float> ans = Diagonals(A, B, 
                                  C, D);
 
    // Print the final answer
    System.out.printf("%.2f %.2f", 
                      (ans.get(0)) + .01, 
                       ans.get(1) + .01);
}
}
 
// This code is contributed by 29AjayKumar

Python3

# Python3 program to implement
# the above approach
 
import math
 
# Function to calculate the length of
# diagonals of a cyclic quadrilateral
def Diagonals(a, b, c, d):
 
    p = math.sqrt(((a * c)+(b * d))*((a * d)+(b * c))
                  / ((a * b)+(c * d)))
    q = math.sqrt(((a * c)+(b * d))*((a * b)+(c * d))
                  / ((a * d)+(b * c)))
 
    return [p, q]
 
 
# Driver Code
A = 10
B = 15
C = 20
D = 25
 
# Function Call
ans = Diagonals(A, B, C, D)
 
# Print the final answer
print(round(ans[0], 2), round(ans[1], 2))

C#

// C# Program to implement
// the above approach
using System;
using System.Collections.Generic;
class GFG{
 
// Function to calculate the length of
// diagonals of a cyclic quadrilateral
static List<float> Diagonals(int a, int b, 
                             int c, int d)
{
  List<float> ans = new List<float>();
  ans.Add((float) Math.Sqrt(((a * c) + (b * d)) * 
                            ((a * d) + (b * c)) / 
                            ((a * b) + (c * d))));
  ans.Add((float) Math.Sqrt(((a * c) + (b * d)) * 
                            ((a * b) + (c * d)) / 
                            ((a * d) + (b * c))));
  return ans;
}
 
// Driver Code
public static void Main(String[] args)
{
  int A = 10;
  int B = 15;
  int C = 20;
  int D = 25;
 
  // Function Call
  List<float> ans = Diagonals(A, B, 
                              C, D);
 
  // Print the readonly answer
  Console.Write("{0:F2} {1:F2}", 
                 (ans[0]) + .01, 
                  ans[1] + .01);
}
} 
 
// This code is contributed by 29AjayKumar

Javascript

<script>
 
// Javascript Program to implement
// the above approach
 
// Function to calculate the length of
// diagonals of a cyclic quadrilateral
function Diagonals(a, b, c, d)
{
 
    var p = parseFloat(
            Math.sqrt(((a * c) + (b * d)) * 
                      ((a * d) + (b * c)) / 
                      ((a * b) + (c * d))));
    var q = parseFloat(
            Math.sqrt(((a * c) + (b * d)) * 
                      ((a * b) + (c * d)) / 
                      ((a * d) + (b * c))));
 
    return [p, q];
}
 
// Driver Code
var A = 10;
var B = 15;
var C = 20;
var D = 25;
 
// Function Call
var ans = Diagonals(A, B, C, D)
 
// Print the final answer
document.write(ans[0].toFixed(2) + " ", 
               ans[1].toFixed(2));
 
// This code is contributed by kirti
 
</script>

Output:

22.06 26.07

Time Complexity: O(log n)
Auxiliary Space: O(1)

Feeling lost in the world of random DSA topics, wasting time without progress? It’s time for a change! Join our DSA course, where we’ll guide you on an exciting journey to master DSA efficiently and on schedule.
Ready to dive in? Explore our Free Demo Content and join our DSA course, trusted by over 100,000 zambiatek!