Designing Kitchens and Bathrooms - Damp patch on bathroom ceiling near fan

I need help to solve this problem.

I live in upstate NY and the weather is now getting colder, we have had a few inches of snow already.

In the last few weeks since the cold weather arrived especially after some snow. I have noticed a damp patch on the bathroom ceiling near the extraction fan.

I have been in the loft and I cannot find any roof leaks. The fan has a flexi hose attached which and goes from the fan to the roof soffet to vent. When I removed the insulation I can see water around the area where the hose attaches to the fan.

I am thinking it is condensation building up inside the hose which is running back towards the fan and sepping out. I did vaccum the fan cover earlier this year to clean it other than that I have not touched it.

Any ideas on what is happening and how to stop it, also to fix the damp spot on the textured ceiling.

Thanks in advance.

Malcolm:(

You're right.
It is condensation (forming in the unheated attic) running back down the uninsulated vent to the exhaust fan.
Wrap the flex vent hose in the attic in insulation batts. Duct tape them in place. Don't crush the insulation.
If the drywall is soft and mushy after it drys, you'll have to cut out the bad part back to the center of ceiling rafters.
If it dries hard, and is just discolored, you can seal the water stain with Kilz or another sealer, and repaint the ceiling.
Good Luck!
Mike

Mike;

Thanks. Would you use the foil pipe insulation and wrap it around or faced batts then duct tape?

The drywall is solid it as only happended hree times and I leave the fan running a few hours to dry it out. So I will apply some Kilz.

Malcolm