I was recently stalked by a cougar while on a hike with my girlfriend for the last mile or so to the car.
You're lucky you're alive.
Sweet Jesus, big cats scare the crap outta me.
The wife and I contribute to Big Cat Rescue in Florida. The last time we were there, they had a cougar nearly as big as an African lion - I had no idea they could get that big. I think it went about 260 lbs.
I've seen the tigers stalk BCR workers - the workers were OUTSIDE the cat enclosures, but it was still scary. I think a 10mm would do the job on cougar, but I'd probably just avoid the area.