Config Geo
Formerly known as "American Geo". This is a unit on geometry problems with a highly traditional or synthetic flavor, for example USAMO 2016/3 and USAMO 2017/3. These sorts of problems were popular on the USA olympiads and team selection tests around 2016 and it is totally not my fault. These particular ones tend to use common or standard configurations as a base and build on top of them, as opposed to starting afresh.
Config Geo is a cousin of Classic Geo; they were once combined in a unit. However, Config Geo is slightly different; in classic geo often you have to find synthetic properties from the start with little to no already-existing structure, yet in config geo the problem is built upon an already rich existing configuration (so it would be slightly easier). On average, it fits right in the middle in terms of D-level geo difficulty.
Should I do this unit?
HELL YEAH! Its one of the most enjoyable otis geometry units. You should have read EGMO Chapters 1-4 and be familiar with the Chapter 4 configs as a prerequisite to make life a lot easier, as this unit dives into challenging problems immediately. At the start of the problem set, there are more noteworthy configs, which you should definitely work through (they are very useful).
Philosophy
There are several fairly recurrent configurations in Olympiad Geometry, simply because they have so many great properties. For most problems in the problem set, the config will either just be waiting for you to recognize (less often), or you will have to add a couple of points related to the config to make it really stand out (more often). Often, though, the config doesn't completely trivialize the problem; you still need to make some actual synthetic observations in conjunction with recognizing the config properties. The three walkthroughs (2015 USA TST P1, 2016 USAMO 3, 2017 USAMO 3) all heavily emphasize this.
Notable Problems
- 2016 USAMO 3: Very hard walkthrough; great for understanding configurations related to the incenter and excenters.
- 2017 USAMO 3: Hard walkthrough; great for understanding more incenter and excenter configs and their duality with the orthocenter.
- 2020 USA TSTST 2: You should be smelling something with points G and Q... What configurations are these part of? Required 5-pointer on DGY.
- 2008 USAMO 2: C'mon don't barybash this...You can do better than that. What config is F from? A nice diagram may help.
- 2022 CHMMC 6: Observe and reap. What config is point L?
- 2004 ISL G7: Don't be scared of "G7". Fun 9-pointer (5pt on Z); this config is a little trickier to recognize.
- 2009 Iran TST 9: The quintessential, infamous Iran Lemma problem. Required 9-pointer on DGY (not required 5pt on Z); it is certainly a must-try. There are two configs hiding...
- 2015 China TST 2 3 An overly dramatic problem combining 3 different configurations, 9 pointer on Z...