The recently concluded Wuhan Nine Test was innovative and challenging, and the research exams in Wuhan never disappoint. Back in my senior year, I had to tackle these problems, but unfortunately, I am now a freshman. 😇
Of course, as a fan of final problem challenges, I still attempted this eighth question, which turned out to be another centroid problem!
2026 Wuhan Nine Test T8The calculations seem to be quite extensive… I hope to find time in a few days to challenge T14’s solid geometry and the subsequent triangles and derivatives.
This inevitably brings back memories of last year, when the same Wuhan Nine Test T8 also featured a centroid problem, which was even more difficult. 
2025 Wuhan Nine Test T8This problem once appeared on the backboard of Class 0, and the forty-five-degree angle still intimidates many.
Looking at the above two problems, I wonder if you have any insights on these centroid problems? 🧐 I remember that in April or May this year, a certain math teacher shared a four-page practice set of circular curve final problems, and while others seemed stuck on the first two pages, I managed to solve them in one class using this approach, haha. You need to know what you are looking for.1. Draw the diagram, mark what can be marked, and then take a walk through the diagram, considering whether to introduce more unknowns like m and n (the ratio of line segments, and relationships related to the other focal radius forming 2a…)2. From the unknowns (a, c, introduced m, n…) deduce the number of constraints needed; generally, n unknowns require n-1 conditions for constraint.3. Conditions are generally provided by special triangles (Pythagorean, cosine, sine…), (draw auxiliary lines) deriving special triangles may involve some geometric techniques (like symmetry, midpoints, similar triangles…).Actually, the above thought process is a type of freedom of thought in solving math problems, but I prefer to call it unknowns, as the concepts of unknowns, variables, and degrees of freedom can differ.This explanation may seem vague, so below are a few more concrete problems.
2025 Nanjing Second Mock T8This paper is back for everyone to see, and I remember this problem took me quite some time back then.
The most important part is the line F’N, which connects the vertical condition and the first definition of the hyperbola; such a dual-purpose auxiliary line is the hardest to discover in plane geometry. 
2025 Wenzhou Third Mock T8This is such a great problem, subtly containing the test maker’s profound understanding of the core techniques of the 2022 New College Entrance Examination Paper T16.
Symmetry often likes to relate to midpoints and angle bisectors, like in problem #1. 
2023 New College Entrance Examination Paper T16These problems seem to have some shadow of this problem.
Look at this ratio relationship, this symmetry, this first definition relationship of 2a; such patterns are often seen in subsequent mock exams. 
2022 National Paper B T11The most outrageous episode, the notoriously difficult problem, but the value of the problem is still high.
Single choice turned into double choice; no math paper from the 22nd year is easy… it would have been better if it were fill-in-the-blank.ヾ(Ő∀Ő๑) It still involves the first definition, midpoints, and vertical lines, using an auxiliary line that connects the vertical and midpoint conditions. If you have carefully reviewed so many problems, you must have gained a lot. However, problem setting is flexible and varied; the test maker has a hundred strange points to challenge students. Don’t fall into rigid thinking patterns just because of a few problems.For example, the following problem, the entire article is just to set up this vinegar dish for a plate of dumplings.
Original WorkThe layout may not be very appealing, but it probably doesn’t stimulate much appetite… it’s an old problem from senior year. The difficulty of the problem is not extremely high, but its elegance is still at an artistic level!!!
It’s a common model, but most people might not have thought about how to link the relationships between the two triangles. This model’s origin is purely a case of a blind cat meeting a dead rat, a sudden flash of inspiration. The source can still refer to the 2022 New College Entrance Examination Paper T16, but I added some thoughts on the incircle and circumcircle in circular curves. The murmurs of military training are finally coming to an end; it has actually been quite easy, but I’ve been busy with many procedures for the start of school. You are right, but tomorrow during the training, I will take the subway. By the way, why is C language so abstract? Ahhh, I feel like I am being strongly alkali-treated.I hope everyone can experience #2-1, sob sob… I feel like I did really well… I have been dragging my feet on posting #2-2, I really enjoy having someone solve my problems.And I really want to go back to Guangzhou. 😢
