Creating a circle following a pattern

To do this, I would create a circle path that will be the outer edge of your tyre. Then create a triangular wedge shape and align this so that it crosses over the top of your circle path, like so:

Then, rotate and copy this wedge around the circle. Press R for the Rotate tool, and holding Alt, click the centre of the circle (it helps if you have Smart Guides turned on). This will bring up the Rotate dialog box — enter an angle number that divides evenly into 360. In this case, I’ve chosen 15, but feel free to experiment. Press Copy to make a copy (who’d have guessed?) — if you then press Ctrl-D (or Cmd-D) this will repeat the last command and add wedges around the circumference of your circle:

Making sure that the circle is the bottom-most layer (it will be if you’ve followed these steps), select all paths, go to the Pathfinder tool and select ‘Minus Front’. This will cut the wedge shapes from the circle:

Finally, if you’re using a later version of Illustrator, if you use the Direct Selection Tool with the path selected, you’ll notice a load of small blue circles appear. Drag one of these and it will add rounded corners to each of the segments. And there you go!

EDIT: I’ve just re-read the question, rather than the first answer, and realised you asked for this for Photoshop, not Illustrator. Oops! I’m going to leave this here as it’s how I would go about it anyway — as with the previous answer, I would create the tyre in Illustrator and then import it into Photoshop.