
06141885
j
2013e.00520
Tabachnikov, Serge
The (un)equal tangents problem.
Am. Math. Mon. 119, No. 5, 398405 (2012).
2012
Mathematical Association of America (MAA), Washington, DC
EN
G95
convex closed plane curve
oval
tangent
doi:10.4169/amer.math.monthly.119.05.398
Given a circumference and a point lying outside of it, it is wellknown 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.
Antonio M. Oller (Zaragoza)