Question 17
Consider the cube $ABCDA'B'C'D'$. The angle bisectors of the angles $\angle A'C'A$ and $\angle A'AC'$ meet $AA'$ and $A'C'$ at points $P$ and $Q$, respectively. The point $M$ is the foot of the perpendicular from $A'$ onto $C'P$ while $N$ is the foot of the perpendicular from $A'$ onto $AS$. The point $O$ is the center of the face $ABB'A'$.
a) Prove that the planes $(MNO)$ and $(AC'B)$ are parallel.
b) Given that $AB = 1$, find the distance between the planes $(MNO)$ and $(AC'B)$.
a) Prove that the planes $(MNO)$ and $(AC'B)$ are parallel.
b) Given that $AB = 1$, find the distance between the planes $(MNO)$ and $(AC'B)$.