Circumradius of a Cyclic Quadrilateral using the length of Sides - GeeksforGeeks

21 Apr, 2021
Given integers A, B, C, and D denoting the length of sides of a Cyclic Quadrilateral, the task is to find the circumradius i.e., the radius of circumcircle of the given cyclic quadrilateral.
Examples:
Input: A = 3, B = 4, C = 5, D= 6Output: 3.29
Input: A = 10, B = 30, C = 50, D = 20Output: 27.78
Approach: Follow the steps below to solve the problem:
Calculate the semiperimeter of the cyclic quadrilateral with sides A, B, C and D by using the equation:
Now, using Parameshvara’s circumradius formula shown below, calculate the radius for the circumcircle:
Below is the implementation of the above approach:
C++14
Java
Python3
C#
Javascript
// C++ program to find circumradius of// a cyclic quadrilateral using sides#include <bits/stdc++.h>using namespace std; // Function to return the circumradius// of a cyclic quadrilateral using sidesdouble Circumradius(int a, int b, int c, int d){         // Find semiperimeter    double s = (a + b + c + d) / 2.0;     // Calculate the radius    double radius = sqrt(((a * b) + (c * d)) *                         ((a * c) + (b * d)) *                         ((a * d) + (b * c)) /                         ((s - a) * (s - b) *                          (s - c) * (s - d)));     return radius / 4;} // Driver Codeint main(){    int A = 3;    int B = 4;    int C = 5;    int D = 6;     // Function call    double ans = Circumradius(A, B, C, D);     // Print the radius    cout << setprecision(3) << ans;     return 0;} // This code is contributed by mohit kumar 29
// Java program to find circumradius of// a cyclic quadrilateral using sidesimport java.util.*; class GFG{ // Function to return the circumradius// of a cyclic quadrilateral using sidesstatic double Circumradius(int a, int b,                           int c, int d){         // Find semiperimeter    double s = (a + b + c + d) / 2.0;     // Calculate the radius    double radius = Math.sqrt(((a * b) + (c * d)) *                              ((a * c) + (b * d)) *                              ((a * d) + (b * c)) /                              ((s - a) * (s - b) *                               (s - c) * (s - d)));     return radius / 4;} // Driver Codepublic static void main(String[] args){    int A = 3;    int B = 4;    int C = 5;    int D = 6;     // Function call    double ans = Circumradius(A, B, C, D);     // Print the radius    System.out.format("%.2f", ans);}} // This code is contributed by 29AjayKumar
# Program to find Circumradius of# a cyclic quadrilateral using sides import math    # Function to return the Circumradius# of  a cyclic quadrilateral using sidesdef Circumradius(a, b, c, d):     # Find semiperimeter    s = (a + b + c + d) / 2     # Calculate the radius    radius = (1 / 4)*math.sqrt(((a * b)+(c * d))*        ((a * c)+(b * d))*((a * d)+(b * c))        /((s-a)*(s-b)*(s-c)*(s-d)))         return radius    # Driver Code # Given sidesA = 3B = 4C = 5D = 6   # Function Call ans = Circumradius(A, B, C, D)    # Print the radiusprint(round(ans, 2))
// C# program to find circumradius of// a cyclic quadrilateral using sidesusing System; class GFG{ // Function to return the circumradius// of a cyclic quadrilateral using sidesstatic double Circumradius(int a, int b,                           int c, int d){         // Find semiperimeter    double s = (a + b + c + d) / 2.0;     // Calculate the radius    double radius = Math.Sqrt(((a * b) + (c * d)) *                              ((a * c) + (b * d)) *                              ((a * d) + (b * c)) /                              ((s - a) * (s - b) *                               (s - c) * (s - d)));     return radius / 4;} // Driver Codepublic static void Main(String[] args){    int A = 3;    int B = 4;    int C = 5;    int D = 6;     // Function call    double ans = Circumradius(A, B, C, D);     // Print the radius    Console.Write("{0:F2}", ans);}} // This code is contributed by 29AjayKumar
<script> // Javascript program to find circumradius of// a cyclic quadrilateral using sides // Function to return the circumradius// of a cyclic quadrilateral using sidesfunction Circumradius(a, b, c, d){         // Find semiperimeter    var s = (a + b + c + d) / 2.0;     // Calculate the radius    var radius = Math.sqrt(((a * b) + (c * d)) *                          ((a * c) + (b * d)) *                          ((a * d) + (b * c)) /                          ((s - a) * (s - b) *                          (s - c) * (s - d)));     return radius / 4;} // Driver codevar A = 3;var B = 4;var C = 5;var D = 6; // Function callvar ans = Circumradius(A, B, C, D); // Print the radiusdocument.write(ans.toFixed(2));     // This code is contributed by Khushboogoyal499 </script>
3.29
Time Complexity: O(1) Auxiliary Space: O(1)
mohit kumar 29
29AjayKumar
khushboogoyal499
Mensuration 2D
Geometric
Mathematical
School Programming
Mathematical
Geometric
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