IMO 1988 LL VIE89

We match sets M of points in the coordinate plane to sets M∗

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IMO 1988 LL VIE89

Origin: VIE

Problem

We match sets M of points in the coordinate plane to sets M∗ according to the rule that (x∗, y∗) belongs to M∗if and only if xx∗+yy∗\leq 1 whenever (x, y) \inM. Find all triangles Y such that Y∗is the reflection of Y at the origin.