4.33. Given two skew lines. Is it possible to draw two intersecting lines such that each of them intersects both given lines?
4.33. Let $p$ and $q$ be two skew lines (Fig. 4.29). Take any point $A$ on line $p$ and connect this point with any two points $B_{1}$ and $B_{2}$ on line $q$. Thus, $A B_{1}$ and $A B_{2}$ are two intersecting lines that intersect both given skew lines.

Answer: Yes, it is possible.

![](https://cdn.mathpix.com/cropped/2024_05_21_1e3d8d2f6605ac23e2a5g-588.jpg?height=505&width=431&top_left_y=109&top_left_x=721)

Fig. 4.29