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: 3.29Input: 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:
- Now, using Parameshvara’s circumradius formula shown below, calculate the radius for the circumcircle:
Below is the implementation of the above approach:
C++14
// 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
// 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 |
Python3
# Program to find Circumradius of# a cyclic quadrilateral using sidesimport 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#
// 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 |
Javascript
<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> |
Output:
3.29
Time Complexity: O(log s)
Auxiliary Space: O(1)
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