Geometry is my weakest point in mathematical olympiads, and I was wondering, if you have experience in this sort of thing, whether I should backtrack to attempt to rebuild my geometry skills at the AIME level, resort to complex and barycentric bash for all geometry questions, or just ignore geometry and pursue the other three fields.
On the USAMO, I can consistently solve all or almost all of the Number theory, Algebra, and Combinatorics questions without fail, maybe missing a NT or Alg question every two sets. Despite this, my Geo is dismal and is probably sub-AIME level. I'm worried that my Geo may be too far gone to try to bring back, since all the time spent there is not spent on the other categories.
I may be better off learning Geo basics, since the MOP requires around 5 questions, and usually there are 2 Geo problems, but again, I've always had a hard time with Geo, and a lot of time would have to go into the area that could be spent in perfecting and expanding other skills as well.
Now the dilemma comes down to: Learning synthetic, Learning bash, or No geo at all. A suggestion from someone with experience would be nice. So far, my mindset has been "avoid geo at all costs and never look back, ever (unless it's a one-step theorem application)."
(I sure wish there was a form of bash that could solve all of geo forever.)
(Book recommendations too if you have any.)