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Draw an angle and label it as $\angle B A C$. Draw its bisector ray $A X$ and take a point $P$ on it. From $P$ draw line segments $P M$ and $P N$, such that $P M \perp A B$ and $P N \perp A C$, where $M$ and $N$ are respectively points on rays $A B$ and $A C$. Measure $P M$ and $P N$. Are the two lengths equal?