holy crap!!! chased by a cougar!!! sounds like a tv episode...
many years ago while hiking on part of the appalachian trail in the smokies, i met a bear once... i got off the trail on one side and he got off on the other... we passed each other about 25' apart...
all the time, we both looked at each others eyes...
when we were passed, and had gone about 50 feet or so, he stopped, turned around and made some sort of noise... i can't describe it, maybe a grunt sorta like a pig, or a snopffing sound... i don't know... maybe it was a snicker

cuz my knees were pretty much jelly... but he went on and i didn't hang around long myself...
problems now are the deer running across the road in front of you... they're having a tuff time in southern KY now as we're in a severe drought and their search for food is bringing them out of the woods...