I encountered a cougar. It was around point #21 in the map (link). The time was around 3:30 PM.

It looked a lot like female lion that I saw from zoo and it was way bigger than normal dog.

It was on the trail and stairing at me from 5 meters apart. I maintained eye contact and backed away slowly for about 5 meters. Luckily another biker coming from opposite direction startled it and it ran away.