AREA OF TRIANGLES ASSOCIATED WITH A STRICTLY LOCALLY CONVEX CURVE Kim, Dong-Soo; Kim, Dong Seo; Bae, Hyun Seon; Kim, Hye-Jung;
It is well known that the area U of the triangle formed by three tangents to a parabola X is half of the area T of the triangle formed by joining their points of contact. Recently, it was proved that this property is a characteristic one of parabolas. That is, among strictly locally convex curves in the plane parabolas are the only ones satisfying the above area property. In this article, we study strictly locally convex curves in the plane . As a result, generalizing the above mentioned characterization theorem for parabolas we present some conditions which are necessary and sufficient for a strictly locally convex curve in the plane to be an open part of a parabola.