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Count of obtuse angles in a circle with ‘k’ equidistant points between 2 given points

A circle is given with k equidistant points on its circumference. 2 points A and B are given in the circle. Find the count of all obtuse angles (angles larger than 90 degree) formed from /_ACB, where C can be any point in circle other than A or B.
Note :
A and B are not equal.
A < B.
Points are between 1 and K(both inclusive).



Examples :

Input : K = 6, A = 1, B = 3.
Output : 1
Explanation : In the circle with 6 
equidistant points, when C = 2 i.e. 
/_123, we get obtuse angle.

Input : K = 6, A = 1, B = 4.
Output : 0
Explanation : In this circle, there 
is no such C that form an obtuse angle.



It can be observed that if A and B have equal elements in between them, there can’t be any C such that ACB is obtuse. Also, the number of possible obtuse angles are the smaller arc between A and B.

Below is the implementation :

C++

// C++ program to count number of obtuse
// angles for given two points.
#include <bits/stdc++.h>
using namespace std;
  
int countObtuseAngles(int a, int b, int k)
{
    // There are two arcs connecting a
    // and b. Let us count points on
    // both arcs.
    int c1 = (b - a) - 1;
    int c2 = (k - b) + (a - 1);
  
    // Both arcs have same number of
    // points
    if (c1 == c2)
        return 0;
  
    // Points on smaller arc is answer
    return min(c1, c2);
}
  
// Driver code
int main()
{
    int k = 6, a = 1, b = 3;
    cout << countObtuseAngles(a, b, k);
    return 0;
}

/div>

Java

// Java program to count number of obtuse
// angles for given two points
class GFG {
  
    static int countObtuseAngles(int a,
                                 int b, int k)
    {
  
        // There are two arcs connecting a
        // and b. Let us count points on
        // both arcs.
        int c1 = (b - a) - 1;
        int c2 = (k - b) + (a - 1);
  
        // Both arcs have same number of
        // points
        if (c1 == c2)
            return 0;
  
        // Points on smaller arc is answer
        return min(c1, c2);
    }
  
    // Driver Program to test above function
    public static void main(String arg[])
    {
  
        int k = 6, a = 1, b = 3;
        System.out.print(countObtuseAngles(a, b, k));
    }
}
  
// This code is contributed by Anant Agarwal.

Python

# C++ program to count number of obtuse
# angles for given two points.
  
def countObtuseAngles( a, b, k):
    # There are two arcs connecting a 
    # and b. Let us count points on
    # both arcs.
    c1 = (b - a) - 1
    c2 = (k - b) + (a - 1)
   
    # Both arcs have same number of
    # points
    if (c1 == c2):
       return 0
       
    # Points on smaller arc is answer
    return min(c1, c2)
   
# Driver code
k, a, b = 6, 1, 3
print countObtuseAngles(a, b, k)
  
# This code is contributed by Sachin Bisht

C#

// C# program to count number of obtuse
// angles for given two points
using System;
  
class GFG {
  
    static int countObtuseAngles(int a,
                           int b, int k)
    {
  
        // There are two arcs connecting
        // a and b. Let us count points
        // on both arcs.
        int c1 = (b - a) - 1;
        int c2 = (k - b) + (a - 1);
  
        // Both arcs have same number
        // of points
        if (c1 == c2)
            return 0;
  
        // Points on smaller arc is 
        // answer
        return Math.Min(c1, c2);
    }
  
    // Driver Program to test above
    // function
    public static void Main()
    {
  
        int k = 6, a = 1, b = 3;
          
        Console.WriteLine(
           countObtuseAngles(a, b, k));
    }
}
  
// This code is contributed by vt_m.

PHP

<?php
// PHP program to count number 
// of obtuse angles for given 
// two points.
  
function countObtuseAngles($a, $b, $k)
{
    // There are two arcs connecting a
    // and b. Let us count points on
    // both arcs.
    $c1 = ($b - $a) - 1;
    $c2 = ($k - $b) + ($a - 1);
  
    // Both arcs have same number of
    // points
    if ($c1 == $c2)
        return 0;
  
    // Points on smaller arc is answer
    return min($c1, $c2);
}
  
// Driver code
$k = 6; $a = 1; $b = 3;
echo countObtuseAngles($a, $b, $k);
  
// This code is contributed by aj_36
?>


Output :

1

Please write comments if you find anything incorrect, or you want to share more information about the topic discussed above.



This article is attributed to GeeksforGeeks.org

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