Question 74
Find the smallest positive integer $k$ with a property: for any three points with integer coordinates on a plane
$$
L_{\max} - L_{\min} \gt \frac{1}{\sqrt{k} \cdot L_{\max}},
$$
where $L_{\max}$ and $L_{\min}$ are respectively maximum and minimum distances among them.
$$
L_{\max} - L_{\min} \gt \frac{1}{\sqrt{k} \cdot L_{\max}},
$$
where $L_{\max}$ and $L_{\min}$ are respectively maximum and minimum distances among them.