Given four positive integers A, B, C, and D representing the sides of a Cyclic Quadrilateral, the task is to find all the interior angles of the cyclic quadrilateral.
A cyclic quadrilateral is a quadrilateral whose vertices lie on a single circle.
This circle is called the circumcircle or circumscribed circle, and the vertices are said to be concyclic(A, B, C, and D).
( In the figure, r is the circumradius and a, b, c, and d are length of AB, BC, CD, and DA respectively).
Examples:
Input: A = 10, B = 15, C = 20, D = 25
Output:
?A: 85.59 degrees
?B: 122.58 degrees
?C: 94.41 degrees
?D: 57.42 degreesInput: A = 10, B = 10, C = 10, D = 10
Output:
?A: 90.00 degrees
?B: 90.00 degrees
?C: 90.00 degrees
?D: 90.00 degrees
Approach: The given problem can be solved by using the formula to calculate the cosine of the interior angle of a cyclic quadrilateral. The formula is given by:
Follow the steps below to solve the problem:
- Store the cosine of each interior angle of the cyclic quadrilateral.
- Find the angle in radians using acos() function.
- Convert the angle in radians to degrees and print the result.
Below is the implementation of the above approach:
C++
// C++ program for the above approach#include <bits/stdc++.h>using namespace std;// Function to find the interior angles// of the cyclic quadrilateralvoid findAngles(double a, double b, double c, double d){ // Stores the numerator and the // denominator to find angle A double numerator = a * a + d * d - b * b - c * c; double denominator = 2 * (a * b + c * d); double x = numerator / denominator; cout << fixed << setprecision(2) << "A: " << (acos(x) * 180) / 3.141592 << " degrees"; // Stores the numerator and the // denominator to find angle B numerator = a * a + b * b - c * c - d * d; x = numerator / denominator; cout << fixed << setprecision(2) << "\nB: " << (acos(x) * 180) / 3.141592 << " degrees"; // Stores the numerator and the // denominator to find angle C: numerator = c * c + b * b - a * a - d * d; x = numerator / denominator; cout << fixed << setprecision(2) << "\nC: " << (acos(x) * 180) / 3.141592 << " degrees"; // Stores the numerator and the // denominator to find angle D: numerator = d * d + c * c - a * a - b * b; x = numerator / denominator; cout << fixed << setprecision(2) << "\nD: " << (acos(x) * 180) / 3.141592 << " degrees";}// Driver Codeint main(){ double A = 10, B = 15, C = 20, D = 25; findAngles(A, B, C, D); return 0;} |
Java
// Java program for the above approachclass GFG{ // Function to find the interior angles// of the cyclic quadrilateralstatic void findAngles(double a, double b, double c, double d){ // Stores the numerator and the // denominator to find angle A double numerator = a * a + d * d - b * b - c * c; double denominator = 2 * (a * b + c * d); double x = numerator / denominator; System.out.println("A: " + Math.round(((Math.acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees"); // Stores the numerator and the // denominator to find angle B numerator = a * a + b * b - c * c - d * d; x = numerator / denominator; System.out.println("B: " + Math.round(((Math.acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees"); // Stores the numerator and the // denominator to find angle C: numerator = c * c + b * b - a * a - d * d; x = numerator / denominator; System.out.println("C: " + Math.round(((Math.acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees"); // Stores the numerator and the // denominator to find angle D: numerator = d * d + c * c - a * a - b * b; x = numerator / denominator; System.out.println("D: " + Math.round(((Math.acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees");}// Driver Codepublic static void main (String[] args){ double A = 10, B = 15, C = 20, D = 25; findAngles(A, B, C, D);}}// This code is contributed by AnkThon |
Python3
# Python3 program for the above approachimport math# Function to find the interior angles# of the cyclic quadrilateraldef findAngles(a, b, c, d): # Stores the numerator and the # denominator to find angle A numerator = a * a + d * d - b * b - c * c denominator = 2 * (a * b + c * d) x = numerator / denominator print("A: ", '%.2f' % ((math.acos(x) * 180) / 3.141592), " degrees") # Stores the numerator and the # denominator to find angle B numerator = a * a + b * b - c * c - d * d x = numerator / denominator print("B: ", '%.2f' % ((math.acos(x) * 180) / 3.141592), " degrees") # Stores the numerator and the # denominator to find angle C: numerator = c * c + b * b - a * a - d * d x = numerator / denominator print("C: ", '%.2f' % ((math.acos(x) * 180) / 3.141592), " degrees") # Stores the numerator and the # denominator to find angle D: numerator = d * d + c * c - a * a - b * b x = numerator / denominator print("D: ", '%.2f' % ((math.acos(x) * 180) / 3.141592), " degrees") # Driver Codeif __name__ == "__main__": A = 10 B = 15 C = 20 D = 25 findAngles(A, B, C, D)# This code is contributed by ukasp |
C#
// C# program for the above approachusing System;class GFG{ // Function to find the interior angles// of the cyclic quadrilateralstatic void findAngles(double a, double b, double c, double d){ // Stores the numerator and the // denominator to find angle A double numerator = a * a + d * d - b * b - c * c; double denominator = 2 * (a * b + c * d); double x = numerator / denominator; Console.WriteLine("A: " + Math.Round(((Math.Acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees"); // Stores the numerator and the // denominator to find angle B numerator = a * a + b * b - c * c - d * d; x = numerator / denominator; Console.WriteLine("B: " + Math.Round(((Math.Acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees"); // Stores the numerator and the // denominator to find angle C: numerator = c * c + b * b - a * a - d * d; x = numerator / denominator; Console.WriteLine("C: " + Math.Round(((Math.Acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees"); // Stores the numerator and the // denominator to find angle D: numerator = d * d + c * c - a * a - b * b; x = numerator / denominator; Console.WriteLine("D: " + Math.Round(((Math.Acos(x) * 180) / 3.141592) * 100.0) / 100.0 + " degrees");}// Driver Codepublic static void Main(string[] args){ double A = 10, B = 15, C = 20, D = 25; findAngles(A, B, C, D);}}// This code is contributed by AnkThon |
Javascript
<script>// JavaScript program for the above approach// Function to find the interior angles// of the cyclic quadrilateralfunction findAngles(a, b, c, d){ // Stores the numerator and the // denominator to find angle A var numerator = a * a + d * d - b * b - c * c var denominator = 2 * (a * b + c * d) var x = numerator / denominator document.write("A: ", Math.round(((Math.acos(x) * 180) / 3.141592) * 100) / 100.0, " degrees"); document.write("<br>"); // Stores the numerator and the // denominator to find angle B numerator = a * a + b * b - c * c - d * d x = numerator / denominator document.write("B: ", Math.round(((Math.acos(x) * 180) / 3.141592) * 100) / 100.0, " degrees"); document.write("<br>"); // Stores the numerator and the // denominator to find angle C: numerator = c * c + b * b - a * a - d * d x = numerator / denominator document.write("C: ", Math.round(((Math.acos(x) * 180) / 3.141592) * 100) / 100.0, " degrees"); document.write("<br>"); // Stores the numerator and the // denominator to find angle D: numerator = d * d + c * c - a * a - b * b x = numerator / denominator document.write("D: ", Math.round(((Math.acos(x) * 180) / 3.141592) * 100) / 100.0, " degrees");} // Driver Code var A = 10var B = 15var C = 20var D = 25 findAngles(A, B, C, D)// This code is contributed by AnkThon</script> |
Output:
A: 85.59 degrees B: 122.58 degrees C: 94.41 degrees D: 57.42 degrees
Time Complexity: O(1)
Auxiliary Space: O(1)
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