Horizontal hangers - clip the ring, not the hanger
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While by far the most common type of bolt hanger is vertical, you may find horizontal hangers (usually with a welded steel ring) that look like this. (These are from the Spanish company Fixe; other companies might make them too.)
The reason for the horizontal hanger is so the ring hangs perpendicular to the rock. This makes it easier to pull your rappel rope.
To be honest, I'm not a big fan of these. The rings can’t be easily replaced when they get worn out, and a downward load can put some strange leverage on the bolt and hanger. A vertical hanger, a quick link, and a welded ring or another quick link does pretty much the same thing and is much easier to replace.
But you will find this flavor of anchor in the wild, so it's good to know what to do with them.
With these horizontal hangers, it's best practice to clip the ring, and NOT the horizontal hanger.
While most of the time it's not a big deal if you do clip the hanger, with certain carabiners in some configurations, the carabiners can get twisted and torqued in a strange way.
I've never heard of one breaking, but it's not optimal. So clip the ring, and you’ll be fine.
More reasons to clip the ring:
Depending on carabiner shape, makes it easier to “clip it and flip it”, so you can arrange your carabiner gate facing down and out
Will never load your carabiner at a strange angle
Accepts a carabiner of any shape and size
Allows the ring to be used to more easily set up a rappel, either by you or someone else, (more on that below)