• Last Updated : 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= 6
Output: 3.29

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

Below is the implementation of the above approach:

## C++14

 // C++ program to find circumradius of // a cyclic quadrilateral using sides #include  using namespace std;   // Function to return the circumradius // of a cyclic quadrilateral using sides 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 = 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 Code int 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

 // Java program to find circumradius of // a cyclic quadrilateral using sides import java.util.*;   class GFG{   // Function to return the circumradius // of a cyclic quadrilateral using sides static 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 Code public 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

## Python3

 # Program to find Circumradius of # a cyclic quadrilateral using sides   import math       # Function to return the Circumradius # of  a cyclic quadrilateral using sides def 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 sides A = 3 B = 4 C = 5 D = 6     # Function Call   ans = Circumradius(A, B, C, D)       # Print the radius print(round(ans, 2))

## C#

 // C# program to find circumradius of // a cyclic quadrilateral using sides using System;   class GFG{   // Function to return the circumradius // of a cyclic quadrilateral using sides static 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 Code public 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

## Javascript

 

Output:

3.29

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

My Personal Notes arrow_drop_up
Recommended Articles
Page :