IMO 1979 LL GDR30

Let M be a set of points in a plane with at least two elements.

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IMO 1979 LL GDR30

Origin: GDR

Problem

Let M be a set of points in a plane with at least two elements. Prove that if M has two axes of symmetry g1 and g2 intersecting at an angle \alpha = q\pi, where q is irrational, then M must be infinite.