5. Andrej and Blaž drew a circle on the playground and marked diametrically opposite points on it. They each stood on one of these points and started walking in opposite directions at a uniform speed. By the time they first met, Andrej had walked 60 m. From the time they first met until they met again, Blaž had walked 90 m. What is the circumference of the drawn circle?

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50th Mathematical Competition for High School Students in Slovenia

Selection Competition, March 29, 2006

## Problems for 2nd Year Students
I/5. Up to the moment they first met, Andrej and Blaž had together walked half the circular path, as they started walking from diametrically opposite points. From the moment they first met until they met again, they had walked the entire circular path. Since they walked at uniform speeds, Andrej had walked $120 \mathrm{~m}$ in this time, which is twice as much as he walked until the first meeting. The circular path was $120+90=210 \mathrm{~m}$ long.

The conclusion that they had walked half the circular path by the first meeting ............ 2 points

The conclusion that they had walked the entire circular path by the second meeting . . . . . . . . 2 points

The conclusion that Andrej had walked 120 m by the second meeting ....................... 2 points

![](https://cdn.mathpix.com/cropped/2024_06_07_fb5898f0472fc84ca82bg-07.jpg?height=51&width=1627&top_left_y=1642&top_left_x=223)