Question 135
Let $ABCA'B'C'$ be a triangular regular prism, with lateral edges $AA'$, $BB'$, $CC'$. Consider the midpoint $D$ of the edge $BC$ and the parallelogram $ADB'E$. Let $F$ be the orthogonal projection of the point $A'$ on the line $AE$, $d$ be the intersection of the planes $(ADE)$ and $(A'CF)$ and $P$ be the intersection of the line $d$ with the plane $(ABC)$. Prove that $P$ is the baricentre of the triangle $ABC$ if and only if $AB = AA'\sqrt{2}$.
Valeriu Bărbieru
Valeriu Bărbieru