I used barycentric coordinates to solve half of a problem. I derived the incenter coordinates and made a bunch of lines and it worked. I read the solution for the other half, not really because I gave up, but because the problem and the solution were next to each other and it was too easy to read.

TRIANGLE CENTERS
Incenter, centroid, circumcenter, orthocenter, nine-point center, Gergonne point, symmedian point, Fermat point. Rooting through Wikipedia references for the Gergonne point you find a paper with 43 theorems, like "The Gergonne point is the perspector of the intouch triangle and the triangle of the reflections of the internal center of similitude of the incenter and the circumcenter in the sides of the excentral triangle." And the scariest bit is I now understand every word there.

THEOREMS I KEEP FORGETTING TO USE
Ptolemy's theorem

Actually, that's it.

STUFF I NEVER GET TO USE
Desargues' theorem
Steiner-Lehmus
Complex number bash
Arrow's theorem (*)

* Yes, it has nothing to do with geometry, or really with anything in the range of high-school contests, but it's awesome.

SOMETHING ELSE
I received my abstract algebra textbook the class I'm in will use. Nothing related to AoPS there, unfortunately. Anyway, much friendlier than last year's.

My math teacher also reports that some of my classmates want to take the AMC 8.

I really wonder too often how much of my personal information a stalker could deduce from this site.

If you read all the way here, please comment just for the heck of it.