KöMaL 2020 B5124

The base of a right pyramid is a square $ABCD$, and the apex of the pyramid is $E$. The skew edges $AB$ and $CE$ are connected by a transversal that is normal to both of them. The feet of the normal transversal are point $P$ on the line segment $AB$, and point $Q$ on the line segment $CE$. Given that $Q$ bisects the edge $CE$, determine the ratio $AP: PB$, and calculate the angle enclosed between the lateral faces and the base of the pyramid.