Question 36
a) If $ABCA'B'C'$ is a right prism and the points $M \in (BC)$, $N \in (CA)$, $P \in (AB)$ are such that the straight lines $A'M$, $B'N$ and $C'P$ are pairwise perpendicular and concurrent, then the prism is regular.
b) If $ABCA'B'C'$ is a regular prism and $\frac{AA'}{AB} = \frac{\sqrt{6}}{4}$, then one can find the points $M \in (BC)$, $N \in (CA)$, $P \in (AB)$ such that the straight lines $A'M$, $B'N$ and $C'P$ are pairwise perpendicular and concurrent.
b) If $ABCA'B'C'$ is a regular prism and $\frac{AA'}{AB} = \frac{\sqrt{6}}{4}$, then one can find the points $M \in (BC)$, $N \in (CA)$, $P \in (AB)$ such that the straight lines $A'M$, $B'N$ and $C'P$ are pairwise perpendicular and concurrent.