Question 10
The altitudes of a tetrahedron $ABCD$ are extended externally to points $A'$, $B'$, $C'$ and $D'$ respectively, where $AA' = k / h_a$, $BB' = k / h_b$, $CC' = k / h_c$ and $DD' = k / h_d$. Here, $k$ is a constant and $h_a$ denotes the length of the altitude of $ABCD$ from vertex $A$, etc. Prove that the centroid of the tetrahedron $A'B'C'D'$ coincides with the centroid of $ABCD$.