Subtract the angles
There is a circle (circumcentre: \( O \); circumference: \( k \)). On \( k \) a random point \( A \) is picked. Now, the point \( B \) is the furthest point from the point \( A \) and it lies on \( k \). Point \( C \) is picked and has the following properties:
\( C \in k \) and \( AB = 2 \times BC \)
After all this, a completely random point \( X \) is picked from \( k \). Find the value of \( \angle BXC \).
Important: Since there are two answers (one is \( \alpha \) and the other one is \( \beta \)), solution shall be \( |\alpha - \beta| \) (in degrees).