Problem

Source: BMO Shortlist 2015 G3 (UK)

Tags: geometry, combinatorial geometry, angles



A set of points of the plane is called obtuse-angled if every three of it's points are not collinear and every triangle with vertices inside the set has one angle $ >91^o$. Is it correct that every finite obtuse-angled set can be extended to an infinite obtuse-angled set? (UK)