Equichordal Point

A point $P$ for which all the Chords passing through $P$ are of the same length. It satisfies

$$px+py={\rm [const]},$$

where $p$ is the Chord length. It is an open question whether a plane convex region can have two equichordal points.

See also Equichordal Problem, Equiproduct Point, Equireciprocal Point