It's easy to get confused by great circle distances when looking at a flat map.
I find it much easier to understand the concept while looking at a globe, or if I don't have any, on Google Earth.
The trick is to rotate the globe and redefine the north pole, so that Monterey is on "top" of the world.
With our new definition:
- Monterey is now the North Pole.
- Every direction is "South".
- Starting from Monterey, every direction is a meridian, and a great circle.
- From any direction, if you keep walking ~20000km, you'll land on the South Pole (= the antipode of Monterey, as mentioned by others)
- Every point on the Equator is ~10000km away from Monterey
- For any given latitude, the points on the parallel will all have the same distance to Monterey.
- If you keep walking ~40000km, in any direction, you'll land back in Monterey.
Once you found an interesting place with this technique, you can use the original latitude/longitude grid to get the correct coordinates.
In comparison, the newly defined "equator" looks like a sine curve on a flat map. The green area is the "northern hemisphere", the white line represents every point 10000km away from Monterey: