Subtract the angles

Geometry Level pending

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).

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