Question 15
In the right parallelepiped $ABCD'A'B'C'D'$, with $AB = 12\sqrt{3}$ cm and $AA' = 18$ cm, we consider the points $P \in [AA']$ and $N \in [A'B']$ such that $A'N = 3B'N$. Determine the length of the line segment $[AP]$ such that for any position of the point $M \in [BC]$, the triangle $MNP$ is right angled at $N$.
Damian Marinescu
Supplemental illustration of the intended rectangular-base case; this extra assumption is discussed separately in the editorial.
Damian Marinescu
Supplemental illustration of the intended rectangular-base case; this extra assumption is discussed separately in the editorial.