Given a circumference and a point lying outside of it, it is well-known that the two tangents to the circumference passing through the given point are equal. In this (very interesting) paper the “opposite” problem (in some sense) is studied. Namely, the author considers a strictly convex closed plane curve (a.k.a. an oval) and tries to find (and asks whether it exists) a set of points (maybe a curve) lying outside it, such that the two tangents to the original oval passing through each of these points are unequal. The author, against previous evidence, is able to construct an oval having the desired property.

Reviewer:

Antonio M. Oller (Zaragoza)