MathDB

A set

M

of points in the plane will be called obtuse, if any 3 points from

M

are the vertices of an obtuse triangle. a.) Prove: For each finite obtuse set

M

there is a point in the plane with the following property:

P

is no element from

M

and

M \cup \{P\}

is also obtuse. b.) Determine whether the statement from a.) will remain valid, if it is replaced by infinite.

Problem Statement