Task 17. Given a regular hexagonal pyramid $M A B C D E F$. Point $K$ bisects edge $B M$. Find the ratio in which the plane $F E K$ divides edge $A M$ (at point $X$).
Solution. We construct the orthogonal projection of the given pyramid, taking the line $F E$ as the projecting line (Fig. 8). The plane $F E K$ is represented by the line $K E$. Since in the figure the segments $K E$ and $M A$ are medians of the triangle $M B E$, then $M X: X A=2: 1$.
![](https://cdn.mathpix.com/cropped/2024_05_21_8debcc8c8285c4d79a3dg-115.jpg?height=502&width=1372&top_left_y=248&top_left_x=340)