Question 176
Consider the rectangular cuboid $ABCD A'B'C'D'$. Denote by $M, N, P$ the midpoints of $[AB]$, $[BC]$ and $[BB']$, respectively. Let $\{O\}$ be the intersection point of lines $A'N$ and $C'M$.
a) Prove that the points $D$, $O$ and $P$ are collinear.
b) Show that $MC' \perp (A'PN)$ if and only if $ABCDA'B'C'D'$ is a cube.
a) Prove that the points $D$, $O$ and $P$ are collinear.
b) Show that $MC' \perp (A'PN)$ if and only if $ABCDA'B'C'D'$ is a cube.