Circunradio de un cuadrilátero cíclico usando la longitud de los lados

Dados los números enteros A, B, C y D que denotan la longitud de los lados de un cuadrilátero cíclico , la tarea es encontrar el circunradio, es decir, el radio del círculo del cuadrilátero cíclico dado.

Ejemplos:

Entrada: A = 3, B = 4, C = 5, D= 6
Salida: 3,29

Entrada: A = 10, B = 30, C = 50, D = 20
Salida: 27,78

Enfoque: siga los pasos a continuación para resolver el problema:

• Calcula el semiperímetro del cuadrilátero cíclico con lados A, B, C y D usando la ecuación:

• Ahora, utilizando la fórmula del circunradio de Parameshvara que se muestra a continuación, calcule el radio del círculo:

A continuación se muestra la implementación del enfoque anterior:

// 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 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 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

# 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# 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

<script>
 
// Javascript program to find circumradius of
// a cyclic quadrilateral using sides
 
// Function to return the circumradius
// of a cyclic quadrilateral using sides
function 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 code
var A = 3;
var B = 4;
var C = 5;
var D = 6;
 
// Function call
var ans = Circumradius(A, B, C, D);
 
// Print the radius
document.write(ans.toFixed(2));
     
// This code is contributed by Khushboogoyal499
 
</script>

3.29

Tiempo Complejidad: O(1) 
Espacio Auxiliar: O(1)