Busy Day on Annulus Court

Disclaimer : It is best to try the first problem before this one, as you need to know the original path length to solve this one. This problem assumes that you have already completed that problem and seen the answer.

It's a new day at 360 Annulus Court; in fact, it's a weekend! Brilli slept in, but he still needs to take his ant for a walk. However, his neighbors have already woken up and cars have started driving around. He can't take his usual path because he spends too much time in the road. Can Brilli and his ant take a path such that their $\frac{\text{road}}{\text{sidewalk}}$ ratio is less than 20% of what it previously was, while still traveling less than 260 meters?

Google Maps View of Annulus Court (sidewalk in gray) .