# An Extremal Property of the Rellot Triangle

@article{Makeev2003AnEP, title={An Extremal Property of the Rellot Triangle}, author={V. Makeev}, journal={Journal of Mathematical Sciences}, year={2003}, volume={113}, pages={816-817} }

AbstractLet
$$K \subset \mathbb{R}^2 $$
be a planar set having unit constant width and piecewise
$$C^2 $$
-smooth boundary. Then the area of the set of the points belonging to at least three diameters of K is at most
$$\sqrt 3 /4$$
, and the area of the set of the points belonging to a unique diameter of K is at least
$$(2\pi - 3\sqrt 3 )/4$$
. In both cases, an equality is attained only if K is the Rellot triangle. Bibliography: 2 titles.