Question 81
Let $ABCD$ be a tetrahedron and $M$ be a variable point on the face $BCD$. The perpendicular from $M$ onto the plane $BCD$ meets the planes $ABC$, $ACD$ and $ADB$ in $M_1$, $M_2$ and $M_3$. Prove that the sum $MM_1 + MM_2 + MM_3$ is constant if and only if the tetrahedron's altitude from $A$ passes through the barycentre of the triangle $BCD$.
Vasile Pop
Vasile Pop