Stefanie Wilson said she almost came face to face with the animal on the trail connecting Queen Esther Drive with Snowtop.
"I did not see the cat, but he and my dog had an altercation," Wilson said in an e-mail describing the incident, which occurred at about 7:15 a.m. "The cat was growling and making high-pitched cat screaming noises. They were loud; I have never heard anything quite like it."
"My dog was going nuts barking, and I was screaming as loud as I could, trying to get him to come back to me," she said. "The cat was about three switchbacks up from the bottom, and was within 30 yards of me."
Wilson said one of her two roughly 100-pound dogs, was leashed at the time.
"Someone alone or with a smaller dog may have been in trouble," she said.
In the Park City area, there is a significant population of deer, which provides mountain lions with abundant prey.
"I was able to get my dog to come back to me," Wilson said. "Between my dog barking, and me screaming, the cat must have decided to take off."
Meanwhile, it was mid-morning June 19 when Alan Ross spotted a mountain lion in his backyard on the 2800 block of Telemark Drive in Solamere.
On June 21, a mountain lion was reportedly spotted in The Colony. The animal was seen at about 8:30 p.m. running underneath a nearby chairlift at The Canyons.
"Normally cougars are more afraid of people than people are of them," said Dave Swenson, a state Division of Wildlife Resources conservation officer. "People in Utah have claimed they have been stalked, mountain bikers and joggers."
But cougars have attacked humans in other states.
"It's always something to keep in the back of your mind, but it sure wouldn't stop me from hiking or mountain biking or enjoying the outdoors," Swenson said. "Nobody knows how many cougar we have in the state of Utah, but I know we have cougar in the mountains all around us."
There have occasional reports of mountain lions in the Park City area for years. But wildlife officials say the elusive cats stay at higher elevations until the winter.
"I've seen them in and around the Snyderville Basin They're usually seen at night, or at dusk or dawn," Swenson said. "Typically what I see, and mainly in the winter, I will see cougar tracks in the snow."
If you encounter a mountain lion, to reduce the risk of an attack:
Do not make eye contact with the animal
Back away from the mountain lion slowly
Do not turn and run, which could trigger a mountain lion's instincts to pursue
Make yourself appear as large as possible