Area of triangles associated with a curve
  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. In this article, we study some properties of $U$ and $T$ for strictly convex plane curves. As a result, we establish a characterization for parabolas. 
Dong-Soo Kim and Kyu-Chul Shim
math.DG