Golden Bear is right ...They are a rare sight on the AT.
So here is what you do...
First don't run at the first sight or scream of a cougar - they rarely expose their presence. Pretend you ran into them and it was an accident.... In short-don't move.
Second talk softly ... continue...say kind things..
Follow this with wine or cheese....Then let them follow you home.... front seat is preferable.
Papa D that most likely was a bobcat if it was close to dusk or dawn