I was curious about how range worked exactly in AOE2. As part of this I decided to do a test with a town center. See https://i.imgur.com/b382XDk.jpg
Observations:
TCs have a orthogonal range of 6. If you want a building (say a tower drop...) to be out of range of a TC you need to leave 7 tiles between it and the TC though.
TCs have a diagonal range of ~6. This translates to 4 tiles diagonally. If you want a building to be out of range of the TC you need to leave at least 5 tiles diagonally between them.
Some diagonal tiles that are in range for the TC are outside of it's line of sight. In my test I used a villager to gain sight of them.
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