Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

Sign up
Here's how it works:
  1. Anybody can ask a question
  2. Anybody can answer
  3. The best answers are voted up and rise to the top

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

share|cite|improve this question
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 $B$.

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.