IMO 1972 LL CZS10

Given five points in the plane, no three of which are collinear,

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IMO 1972 LL CZS10

Origin: CZS

Problem

Given five points in the plane, no three of which are collinear, prove that there can be found at least two obtuse-angled triangles with vertices at the given points. Construct an example in which there are exactly two such triangles.