Type: Article

A characteristic property of the Euclidean disc

Jerónimo-Castro, Jesús; Roldán-Pensado;

Abstract:

In this paper the following is proved: Let $K\subset {\Bbb E}^2$ be a smooth strictly convex body, and let $L\subset{\Bbb E}^2$ be a line. Assume that for every point $x\in L\sbs K$ the two tangent segments from $x$ to $K$ have the same length, and the line joining the two contact points passes through a fixed point in the plane. Then $K$ is a Euclidean disc