MathNet 2025 — 50 problems — Part 01 Question 4

Point $P$ lies inside square $ABCD$ such that the areas of $\triangle PAB$, $\triangle PBC$, $\triangle PCD$, and $\triangle PDA$ are $1$, $2$, $3$, and $4$, in some order. Compute $PA \cdot PB \cdot PC \cdot PD$.