Question 114
$A$ puts $5$ points on the plane such that no three of them are collinear. $B$ adds a sixth point that is not collinear with any two of the former points. $A$ wants to eventually construct two triangles from the six points such that one can be placed inside another. Can $A$ put the $5$ points in such a manner so that he would always be able to construct the desired triangles? (We say that triangle $\triangle_1$ can be placed inside triangle $\triangle_2$ if $\triangle_1$ is congruent to a triangle that is located completely inside $\triangle_2$.)