Question 38
The points $T, A, B, C$ are non-coplanar and the straight lines $a, b, c$ are the parallels from the centroid $G$ of the triangle $ABC$ to the straight lines $TA, TB$, respectively $TC$. Let $\{A'\} = a \cap (TBC)$, $\{B'\} = b \cap (TAC)$ and $\{C'\} = c \cap (TAB)$.
a) Prove that $(A'B'C') \parallel (ABC)$.
b) Compute the distance between the planes $(A'B'C')$ and $(ABC)$ as a function of the distance $a$ from $T$ to the plane $(ABC)$.
a) Prove that $(A'B'C') \parallel (ABC)$.
b) Compute the distance between the planes $(A'B'C')$ and $(ABC)$ as a function of the distance $a$ from $T$ to the plane $(ABC)$.