Question 89
Let $P$ be a point in the interior of triangle $A B C$. Lines $A P, B P, C P$ intersect sides $B C, C A, A B$ at $L, M, N$, respectively. Prove that
$$
A P \cdot B P \cdot C P \geq 8 P L \cdot P M \cdot P N .
$$
$$
A P \cdot B P \cdot C P \geq 8 P L \cdot P M \cdot P N .
$$