  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 consider whether this property and
similar ones characterizes parabolas. As a result, we present three conditions
which are necessary and sufficient for a strictly convex curve in the plane to
be an open part of a parabola.
