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Symmetric convex figure

Source: Finnish Mathematics Competition 2002, Final Round, Problem 4

November 14, 2011
combinatorics unsolvedcombinatorics

Problem Statement

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