# 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.
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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

 ` `

Output :

`1`

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Improved By : vt_m, jit_t

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