Theorem: If a closed smooth convex curve (c) in E2 and an interior point O have the property that (c) possesses parallel supporting lines at the endpoints of every chord through O, then the (c) is centrosymmetric and O is the center.
Theorem: If a closed smooth convex curve (c) in E2 and an interior point O have the property that (c) possesses parallel supporting lines at the endpoints of every chord through O, then the (c) is centrosymmetric and O is the center.