Extremal Banach-Mazur distance between a symmetric convex body and an arbitrary convex body on the plane

We prove that if $K, L \subset \mathbb{R}^2$ are convex bodies such that $L$ is symmetric and the Banach-Mazur distance between $K$ and $L$ is equal to $2$, then $K$ is a triangle.Comment: 17 pages, 13 figure