# prove that a point x is on the line perpendicular bisector of segment AB if and only if X…

prove that a point x is on the line perpendicular bisector of segment AB if and only if X is the center of a circle through points A and B

I'm unsure how to prove this. I will ask questions is the proof provided I cant understand thank you

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Show us how far have you gotten yourself. It is easier for members to give an answer if they know what you already know and what you can understand. –  Lazar Ljubenović Feb 6 '13 at 20:59

Hint: If $X$ is the middle point of $AB$, it is obvious. Otherwise, consider two rectangular triangles $\triangle AMX$ and $\triangle BMX$, where $M$ is the middle point of $AB$. Prove (using congruence) that $X$ is equidistant from $A$ and $B$.