FI-MO 2002 Problem 4

Convex figure $\mathcal{K}$ has the following property: if one looks at $\mathcal{K}$ from any point of the certain circle $\mathcal{Y}$ , then $\mathcal{K}$ is seen in the right angle. Show that the figure is symmetric with respect to the centre of $\mathcal{Y.}$