# 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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