$ (C)$ and $(C')$ are two circles which intersect in $A$ and $B$. $(D)$ is a line that moves and passes through $A$, intersecting $(C)$ in P and $(C')$ in P'. Prove that the bisector of $[PP']$ passes through a non-moving point.
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Tags: geometry, perpendicular bisector, geometry unsolved
$ (C)$ and $(C')$ are two circles which intersect in $A$ and $B$. $(D)$ is a line that moves and passes through $A$, intersecting $(C)$ in P and $(C')$ in P'. Prove that the bisector of $[PP']$ passes through a non-moving point.