Flat Earthers and what to do with them

I've spent the last three months in the company of a flat-earther, so I'm a little consoled to find I'm not the only one who has to deal with this errant nonsense.

Highlights as follows:

• "If the earth isn't flat, then why do planes take-off and climb, rather than flying close to the surface?"
  
• "GPS doesn't work in the southern hemisphere."
  
• "If the sun is 93 million miles away, how come you can see it with the naked eye?"
  
• "The moon is transparent: if you look at it during the day, you can see patches of blue the same as the sky!"
  
• "We never landed on the moon [obvs]: the earth is protected from the sun's radiation by a shield right? And a rocket went through that?"
  
  

And there was something about how fast the earth is supposed to spin and how fast it's supposed to orbit the sun, but I'm not sure what the point was as I was trying to stem the bleeding from my ears.

He's also a bit of a cunt, but that may be unrelated.