8. Two towers are of heights $20 \mathrm{~m}$ and $30 \mathrm{~m}$. The top of each tower is connected to the base of the other with a taut wire. At what height above the ground do the two wires cross if the distance between the towers is $40 \mathrm{~m}$?
8. 

![](https://cdn.mathpix.com/cropped/2024_05_30_5f1c108ea9147169b9fdg-3.jpg?height=534&width=600&top_left_y=338&top_left_x=454)

According to the K-K theorem on similarity, it follows that $\triangle A C B \sim \triangle F C E$. 2 POINTS

From the similarity, it follows that $20: x = 40 : y$ or $y = 2x$. 2 POINTS

According to the K-K theorem on similarity, it follows that $\triangle A C D \sim \triangle A F E$. 2 POINTS

From the similarity, it follows that $30 : x = 40 : (40 - y)$ or $30 : x = 40 : (40 - 2x)$ 1 POINT, so $x = 12$.

The two wires intersect at a height of 12 meters above the ground.

2 POINTS

TOTAL 10 POINTS