279. Motorcyclists again. Here is another case involving the motorcyclists mentioned in the previous puzzle. On the map segment (see figure), three roads form a right-angled triangle. When asked about the distance between $A$ and $B$, one of the motorcyclists replied that after he traveled from $A$ to $B$, then to $C$, and back to $A$, the speedometer showed 60 km. The second motorcyclist added that he happened to know that $C$ is 12 km from the road connecting $A$ with $B$, that is, from point $D$ (the dashed line in the figure). Then the person asking, after making a very simple calculation in his mind, said:

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-083.jpg?height=523&width=1106&top_left_y=795&top_left_x=475)

- It's clear, from $A$ to $B \ldots$

Could the reader also determine this distance so quickly?
279. The distances are shown in the figure. The person asking the question only needed to square the 60 km traveled by the first motorcyclist (3600), and divide the result by twice the sum of these 60 and 12 km, which is the distance from road \(A B\) to \(C\), i.e., by 144. Doing the calculations in his head, he, of course, noticed that

![](https://cdn.mathpix.com/cropped/2024_05_21_56f37ca27ac3d928838dg-240.jpg?height=517&width=1122&top_left_y=1700&top_left_x=478)

the result could be obtained by dividing 300 by 12, and therefore immediately found the correct answer - 25 km. I do not show here how to determine, if necessary, the other distances; it is quite easy to do.