You are standing on the surface of earth.
You walk one mile south, then you walk one mile west, then you walk one mile north and you are back where you started.
Where are you?
I‘ ve made some calculations for the general case with arbitrary distance Z for the 3 legs of the trip, instead of 1 mile. The calculations are made for an idealized Earth as a perfect sphere, with radius R = 6400 km. See the first figure for the meaning of the different symbols, the drawing is not to scale!
The trip starts anywhere on the upper circle with radius r2, goes southwards along a meridian over a distance Z km, then westwards along a circle with circumference Z and radius