Question 70
Consider the regular hexagon $ABCDEF$ and a point $S$ outside the plane $(ABC)$, so that $SB = SO = SF$, where $O$ is the center of the hexagon. Let $M, N, P, Q$, respectively $R$ be the orthogonal projections of $A$ onto the straight lines $SB, SC, SD, SE$ respectively $SF$.
Prove that the points $A, M, N, P, Q$ and $R$ are coplanar and find the measure of the angle of the straight lines $QR$ and $SD$.
Supplemental coordinate illustration (AI); perspective is not to scale.
Prove that the points $A, M, N, P, Q$ and $R$ are coplanar and find the measure of the angle of the straight lines $QR$ and $SD$.
Supplemental coordinate illustration (AI); perspective is not to scale.