These are videos of a Google Earth plotting of great circle bearings at 10 degree intervals to Mecca. The results are somewhat non-intuitive.

As well as Mecca there are three other locations on the globe where the lines coalesce at a point - the two poles and the location directly opposite Mecca; Anti-Mecca

Exactly at the north pole ALL directions are south (one remembers the conundrum of the colour of the bear) including Mecca, and bearings are meaningless, and similarly at the south pole all directions are north. At Anti-Mecca any direction will face Mecca

I am not sure many Muslims realise that there is this very special location where they don’t need to bother to pray in any particular direction - all of them are correct! It turns out to be near enough a coral atoll in the French Polynesia South Pacific called Tematagi with 58 inhabitants, near the French nuclear test site at Moruroa Atoll.

Similarly there are two locations where the bearing is substantially the same over a huge area of 2,000,000 square miles - the Amazon basin and Indonesia.

With thanks to E A Reeves and his 1935 ‘Rugby Diagram’ which did the same thing for the bearing of Rugby wireless station, and got me interested in this subject! The *.kmz file which will display in your own copy of GE is available for a small fee.