Question 76
Denote $T$ the center of the face $CDHG$ of the cube $ABCDEFGH$ and consider the points $N \in (AD)$, $U \in (FG)$ so that $\frac{AN}{AD} = \frac{FU}{FG} = \frac{1}{3}$.
Let $P \in (CN)$, $R \in (CU)$ and $Q \in (BE)$ so that $\frac{NP}{NC} = \frac{UR}{UC} = \frac{BQ}{BE} = \frac{1}{4}$ and $S \in (EH)$ so that $\frac{SE}{EH} = \frac{3}{16}$.
Prove that $SPQRT$ is a regular pyramid.
Supplemental coordinate illustration (AI); perspective is not to scale.
Let $P \in (CN)$, $R \in (CU)$ and $Q \in (BE)$ so that $\frac{NP}{NC} = \frac{UR}{UC} = \frac{BQ}{BE} = \frac{1}{4}$ and $S \in (EH)$ so that $\frac{SE}{EH} = \frac{3}{16}$.
Prove that $SPQRT$ is a regular pyramid.
Supplemental coordinate illustration (AI); perspective is not to scale.