# 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;` `}` |

## 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` `?>` |

## Javascript

`<script>` `// Javascript 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.` ` ` `var` `c1 = (b - a) - 1;` ` ` `var` `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` ` ` `var` `k = 6, a = 1, b = 3;` ` ` `document.write(countObtuseAngles(a, b, k));` `// This code is contributed by todaysgaurav` `</script>` |

**Output :**

1

Time Complexity: O(1)

Auxiliary Space: O(1)

This article is contributed by **Aarti_Rathi** and **Rohit Thapliyal**. If you like GeeksforGeeks and would like to contribute, you can also write an article using write.geeksforgeeks.org or mail your article to review-team@geeksforgeeks.org. See your article appearing on the GeeksforGeeks main page and help other Geeks.

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