Given a circle having two chords of equal length. The angle subtended by one of the chords to the centre is given. The task here is to find the measure of the angle subtended by another chord at the centre.
Examples:
Input: 48 Output: 48 degrees Input: 82 Output: 82 degrees
Approach:
Let AC & BD are the two equal chords of the circle having center at O.let the angle subtended by the chord AC be x degrees.
now,
in triangle AOC & BOD,
AO = OB(radii of same circle)
AB = CD(equal chords)
OC = OD(radii of same circle)
so, the triangles AOC & BOD are congruent to each other
so, angle AOC = angle BOD
Equal chords of a circle subtend equal angles at the centre.
Below is the implementation of the above approach:
C++
// C++ program to find the angle// subtended at the center by the chord// when the angle subtended at center// by another chord of equal length is given#include <bits/stdc++.h>using namespace std;void angleequichord(int z){ cout << "The angle subtended at the center is " << z << " degrees" << endl;}// Driver codeint main(){ int z = 48; angleequichord(z); return 0;} |
Java
// Java program to find the angle// subtended at the center by the chord// when the angle subtended at center// by another chord of equal length is givenimport java.io.*;class GFG { static void angleequichord(int z){ System.out.println ( "The angle subtended at the center is "+ z + " degrees");}// Driver codepublic static void main (String[] args) { int z = 48; angleequichord(z);}}// This code is contributed by ajit. |
Python3
# Python3 program to find the angle # subtended at the center by the chord # when the angle subtended at center # by another chord of equal length is given def angleequichord(z) : print("The angle subtended at", "the center is", z ,"degrees" );# Driver code if __name__ == "__main__" : z = 48; angleequichord(z); # This code is contributed by AnkitRai01 |
C#
// C# program to find the angle// subtended at the center by the chord// when the angle subtended at center// by another chord of equal length is givenusing System; class GFG { static void angleequichord(int z){ Console.WriteLine( "The angle subtended at the center is "+ z + " degrees");}// Driver codepublic static void Main (String[] args) { int z = 48; angleequichord(z);}}/* This code contributed by PrinciRaj1992 */ |
Javascript
<script>// JavaScript program to find the angle // subtended at the center by the chord // when the angle subtended at center // by another chord of equal length is given function angleequichord(z) { document.write("The angle subtended at the center is " + z + " degrees" + "<br>"); } // Driver code let z = 48; angleequichord(z); // This code is contributed by Surbhi Tyagi.</script> |
Output:
The angle subtended at the center is 48 degrees
Time Complexity: O(1)
Auxiliary Space: O(1)
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