  Archimedes showed that the area between a parabola and any chord $AB$ on the
parabola is four thirds of the area of triangle $\Delta ABP$, where P is the
point on the parabola at which the tangent is parallel to the chord $AB$.
Recently, this property of parabolas was proved to be a characteristic property
of parabolas. With the aid of this characterization of parabolas, using
centroid of triangles associated with a curve we present two conditions which
are necessary and sufficient for a strictly locally convex curve in the plane
to be a parabola.
