What Geometry Tricks Weekly Actually Is
It's a compilation of shortcut methods for solving geometric problems faster than the standard textbook approach. The core idea is straightforward: for any given shape or problem type, there are often multiple valid solution paths, and some of them are significantly quicker depending on what information you already have. The collection organizes these by shape and problem category rather than by difficulty level. I first ran into this when I was grading high school geometry competitions. Students who knew the standard proofs were scoring around 70% on timed sections. Those who'd memorized the trick set were consistently clearing 90%. The difference wasn't intelligence. It was knowing that a triangle with a 30-60-90 angle configuration has properties that let you skip the law of sines entirely.
Geometry Tricks Weekly: Where to Find It
The most complete version circulates on math competition forums and is also available through several educational archive sites. I use the PDF hosted on the AoPS community wiki since it's the most frequently updated. The original weekly format came from a retired competition coach who compiled them during his tenure at a regional olympiad prep program. You can usually find a direct download link in the pinned posts of the relevant geometry discussion threads. Most of the shortcuts boil down to either recognizing a special configuration or applying a lesser-known theorem that collapses several steps into one. The most commonly used ones fall into three categories: angle chasing shortcuts, area calculation bypasses, and coordinate geometry optimizations. For angle chasing, the trick is memorizing which cyclic quadrilateral properties to invoke immediately. If four points lie on a circle, opposite angles sum to 180 degrees. That alone eliminates half the problems where students waste ten minutes trying to compute individual angles through triangles. I once watched a student spend twelve minutes solving for every angle in a complex configuration when recognizing that two inscribed angles subtended the same arc would have given the answer in thirty seconds.
The area shortcuts are where the real time savings happen. Heron's formula is standard but computationally heavy for contest timing. The coordinate version using the shoelace method is faster if you already have vertex coordinates. For triangles specifically, if you know two sides and the included angle, the area is simply one-half ab sin(C). That formula appears in most textbooks but students rarely think to reach for it under time pressure. Coordinate geometry tricks are the most underrated section. Setting up a problem with strategic coordinates instead of deriving everything through synthetic geometry can reduce a five-step proof to a two-step calculation. Place the right angle of a right triangle at the origin. Place one leg along the x-axis. Suddenly distance formulas become trivial. This approach fails when the problem involves circles or curves that don't align with the axes, which happens more often than you'd think in competition settings.
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When the Tricks Fail
Here's the part nobody mentions: these shortcuts are useless if you can't recognize which one applies. I've seen students who memorized every trick in the collection and still scored poorly because they couldn't identify the underlying configuration. The tricks are pattern recognition tools, not replacement for understanding. If you don't know why a trick works, you'll apply it incorrectly half the time. There's also a hard limit on how far these tricks go. For olympiad-level geometry problems, the configurations are often novel enough that no pre-memorized shortcut applies. The tricks excel at AIME and contest-level problems where standard configurations repeat. At the IMO level, you're mostly on your own regardless of how many tricks you know. Another practical limitation: the compilation includes some methods that only save time if you've already internalized them. A trick that takes thirty seconds to recall is fast. A trick that takes three minutes to derive on the spot is slower than just using the standard approach. I learned this the hard way during a regional competition when I spent six minutes reconstructing the exact configuration for a power of a point trick that I'd only vaguely memorized. The other team members who stuck to fundamentals finished ahead of me.
How to Actually Use This Material
Don't read through the whole collection and expect retention. Work through it problem by problem. Pick a trick, work ten practice problems using only that method until the application becomes automatic, then move on. Spaced repetition matters more than volume. Reviewing the same three tricks weekly for a month produces better results than cramming all forty in a single sitting. The most practical subset to prioritize covers these areas: angle bisector theorem applications, median length formulas, the lemma on angle bisectors in triangles, mass point geometry for ratio problems, and the basic power of a point configurations. These five categories appear in roughly sixty percent of competition geometry problems and the learning curve is manageable. If you're preparing for a specific exam, check whether the test allows calculator use. Several of the coordinate-based shortcuts lose their advantage when you can plug coordinates directly into a calculator. In those cases, synthetic geometry tricks remain more valuable. I switched my preparation strategy completely when I realized my target exam was calculator-optional rather than calculator-required. Everything shifted toward pure geometry methods instead of coordinate approaches.
The collection also includes a few older tricks based on constructions that modern competitions rarely use. Don't waste time on those. The material from 2018 onward is generally more relevant to current competition formats. Anything older tends to reflect problem styles that have been phased out. If you want to get a copy of the current Geometry Tricks Weekly compilation, the most reliable source is the archived document on the competition math forums. Newer editions get posted after each major competition season when new problem types surface and the existing shortcuts get validated or discarded based on actual usage.
