Hehe...

There's a well-traveled 3-way intersection on one path I frequently ride, and it worries me every time I approach it even if I don't see anyone coming.

As far as the OP's left turn being "obvious" because of his friends, there really is no way to reliably know who's riding with whom out there on the path. Anyone could guess that the first two riders were together while the third was going separately, or two just happen to be going in the same direction, etc etc. Those guesses would be wrong, of course, but they're still attempts at making informed decisions.

When turning on a path, it only takes a half-second to completely block the other side; that's nowhere near enough time for a passing rider to react when they don't imagine it happening.

Back out on the street while driving a car, remember that a three-way intersection where a car's trying to turn left (say, a two-lane busier street with a smaller residential street coming from just one side) will often have some passing space on the right side for cars to get past while a left-turning car is waiting for a space in traffic.

Hate to say it, but I think both parties screwed up this time:

- The OP for not "checking his six" and not giving some kind of signal;

- The passing cyclist for not slowing at an intersection and/or passing in front of a potential right hook instead of going around the outside.

I gotta ask the OP, though -- in the moment before making the turn, were you edging left on the path, or were you edging to the right side before turning, hoping to make a wider-radius turn? I could imagine the oncoming rider getting confused if you had gone wide to the right; he could've thought that you were moving to the side to let him pass. If you were moving left (even spending a couple/few seconds in the oncoming lane if traffic allowed), he would make a better guess that you were going to turn left off the path.