Given a circle having a chord and an angle subtended by chord on center of the circle. The task here is to find the measure of the angle subtended by given chord on the circumference.
Examples:
Input:= 90Output: ABC = 45.00 degreesInput:
Approach:
- Let AC be an chord of a circle with centre O, and let C be any point on the circumference anywhere.
- Let, angle AOC(on center) is the given
. - So angle should be on the circumference,
angle ABC = angle AOC/2
An angle at the circumference of a circle is the half angle at the center subtended by the same chord.
Below is the implementation of the above approach:
C++
// C++ Program to calculate angle // on the circumference subtended // by the chord when the central angle// subtended by the chord is given#include <iostream>using namespace std;float angleOncirCumference(float z){ return (z / 2);}// Driver codeint main() { // Angle on center float angle = 65; float z = angleOncirCumference(angle); cout << "The angle is " << (z) << " degrees"; return 0;}// This code is contributed by jit_t |
Java
// Java Program to calculate angle on the circumference// subtended by the chord when the central angle// subtended by the chord is givenclass GFG { static float angleOncirCumference(float z) { return (z / 2); } // Driver code public static void main(String[] args) { // Angle on center float angle = 65; float z = angleOncirCumference(angle); System.out.println("The angle is " + z + " degrees"); }} |
Python3
# Python3 Program to calculate angle # on the circumference subtended # by the chord when the central angle# subtended by the chord is givendef angleOncirCumference(z): return (z / 2);# Driver code# Angle on centerangle = 65;z = angleOncirCumference(angle);print("The angle is", (z), "degrees");# This code is contributed by Rajput-Ji |
C#
// C# Program to calculate angle on the circumference// subtended by the chord when the central angle// subtended by the chord is given using System; public class GFG { static float angleOncirCumference(float z) { return (z / 2); } // Driver code public static void Main(String[] args) { // Angle on center float angle = 65; float z = angleOncirCumference(angle); Console.WriteLine("The angle is " + z + " degrees"); }}// This code is contributed by Rajput-Ji |
Javascript
<script>// JavaScript Program to calculate angle // on the circumference subtended // by the chord when the central angle // subtended by the chord is given function angleOncirCumference(z) { return (z / 2); } // Driver code // Angle on center let angle = 65; let z = angleOncirCumference(angle); document.write("The angle is " + (z) + " degrees"); // This code is contributed by Surbhi Tyagi.</script> |
Output
The angle is 32.5 degrees
Time Complexity: O(1)
Auxiliary Space: O(1)
APPROACH 2 :-
Another approach to find the measure of the angle subtended by a chord on the circumference of a circle, given the central angle subtended by the chord, is as follows:
- Let ???? be the central angle in degrees.
- Convert ???? from degrees to radians by multiplying it by /180 .
- Since the angle subtended on the circumference is half the angle at the center, calculate the angle on the circumference (α) using the formula α = ????/2 .
- Convert α from radians to degrees by multiplying it by 180/ .
- The resulting value is the measure of the angle subtended by the chord on the circumference.
Below is the implementation of the above approach:
C++
#include <iostream>#include <iomanip>#include <cmath>#define PI 3.141float angle_on_circumference(float theta) { float theta_rad = theta * PI / 180; float alpha_rad = theta_rad / 2; float alpha_deg = alpha_rad * 180 / PI; return alpha_deg;}int main() { float central_angle = 65; float angle_subtended = angle_on_circumference(central_angle); std::cout << "The angle is " << std::fixed << std::setprecision(2) << angle_subtended << " degrees" << std::endl; return 0;} |
Java
import java.text.DecimalFormat;public class GFG { static final double PI = 3.141; // Function to calculate the angle subtended by a // central angle on the circumference of a circle static double angleOnCircumference(double theta) { double thetaRad = theta * PI / 180; // Convert angle from // degrees to radians double alphaRad = thetaRad / 2; // Calculate half of the angle in radians double alphaDeg = alphaRad * 180 / PI; // Convert the half-angle // back to degrees return alphaDeg; } public static void main(String[] args) { double centralAngle = 65; // Given central angle in degrees double angleSubtended = angleOnCircumference( centralAngle); // Calculate the subtended angle DecimalFormat df = new DecimalFormat("0.00"); System.out.println( "The angle is " + df.format(angleSubtended) + " degrees"); // Print the result with two // decimal places }} |
Python
import mathdef angle_on_circumference(theta): """ Calculate the angle subtended by a chord on the circumference of a circle. Args: theta (float): The central angle in degrees. Returns: float: The angle subtended by the chord in degrees. """ theta_rad = theta * math.pi / 180 # Convert the central angle from degrees to radians alpha_rad = theta_rad / 2 # Calculate half of the central angle in radians alpha_deg = alpha_rad * 180 / math.pi # Convert the half angle from radians to degrees return alpha_degdef main(): """ Main function to calculate and display the angle subtended by a chord on the circumference of a circle. The central angle is given as 65 degrees, and the angle subtended by the chord is calculated and displayed. """ central_angle = 65 angle_subtended = angle_on_circumference(central_angle) print(f"The angle is {angle_subtended:.2f} degrees")if __name__ == "__main__": main()# This code is contributed by sarojmcy2e |
C#
using System;class GFG { const float PI = 3.141f; // Function to calculate the angle subtended on the // circumference static float AngleOnCircumference(float theta) { float thetaRad = theta * PI / 180; float alphaRad = thetaRad / 2; float alphaDeg = alphaRad * 180 / PI; return alphaDeg; } static void Main() { float centralAngle = 65; float angleSubtended = AngleOnCircumference(centralAngle); // Print the calculated angle with 2 decimal places Console.WriteLine("The angle is " + angleSubtended.ToString("F2") + " degrees"); }} |
Javascript
// Define a constant for PIconst PI = 3.141;// Function to calculate the half of an angle on the circumference in degreesfunction angle_on_circumference(theta) { // Convert the input angle from degrees to radians const theta_rad = theta * (PI / 180); // Calculate the half angle in radians const alpha_rad = theta_rad / 2; // Convert the half angle back to degrees const alpha_deg = alpha_rad * (180 / PI); // Return the result return alpha_deg;}// Main functionfunction main() { // Define the central angle in degrees const central_angle = 65; // Calculate the half angle subtended by the central angle const angle_subtended = angle_on_circumference(central_angle); // Display the result with two decimal places console.log(`The angle is ${angle_subtended.toFixed(2)} degrees`);}// Call the main function to execute the programmain(); |
Output
The angle is 32.50 degrees
Time Complexity: O(1)
Auxiliary Space: O(1)
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