A curve such that all perpendicular bisectors of its chords are concurrent

Question

Of course a circle is an example. Is there any other example other than a circle?

A chord is the line segment joining two points on a curve.

Answer 1

No. If $P,Q,R$ are three distinct points on the curve and the perpendicular bisectors of $PQ$ and $QR$ meet at $O$, then $O$ is the circumcenter of $PQR$ and $OP=OQ=OR$. In particular, if the given property holds, every point on the curve has the same distance from $O$. If the curve is closed, it is a circle for sure.