# Math Genius: angles and points interior and exterior to them

Let $$xOz$$ be an angle, let $$A$$ be a random point on the plane. Define the
interior of the angle $$xOz$$ to be the intersection of the semiplanes
$$(Ox, A)$$ and $$(Oz, A)$$. By this definition it follows directly that $$A$$ is
considered “internal” to the angle $$xOz$$. Now, let $$B$$ be a point external
to the angle (i.e. a point not belonging to the intersection of the semiplanes $$(Ox, A)$$ and $$(Oz, A)$$. Prove that the line segment $$AB$$ must cut through one of
the sides of the angle $$xOz$$.