Question 19
Let $P_0, P_1, P_2, \dots, P_n$ be $n+1$ points on a plane, and the minimum distance between each two points of them is $d$ ($d \gt 0$). Prove
$$
| P_0 P_1 | \cdot | P_0 P_2 | \cdots | P_0 P_n | \gt \left( \frac{d}{3} \right)^n \sqrt{(n+1)!}
$$
$$
| P_0 P_1 | \cdot | P_0 P_2 | \cdots | P_0 P_n | \gt \left( \frac{d}{3} \right)^n \sqrt{(n+1)!}
$$