Hi! Here's another geometry problem I'm thinking about, and I would appreciate any help with a proof. Thanks in advance!

Let AD and BE be the altitudes of an acute triangle ABC, with D on BC and E on AC. The line DE intersects the circumcircle of triangle ABC again at two points M and N. Prove that CM = CN.

Thanks for your time and help!

In the acute triangle with , the foot of altitudes from to the sides are , respectively. is the orthocenter. is the midpoint of segment . Lines and intersect at . Let the tangents drawn to circumcircle from and intersect at . Prove that are colinear

Hey! People are starting to get their swag packages from Jane Street for qualifying for USA(J)MO, and after some initial discussion on what we got, people are getting different things. Out of curiosity, I was wondering how they decide who gets what.
Please enter the following info:

- USAMO or USAJMO
- Grade
- Score
- Award/Medal/HM
- MOP (yes or no, if yes then color)
- List of items you got in your package

I will reply with my info as an example.

I don’t understand the solution. I got 220 as answer. Why does it insist, for example two primes must add to the third, when you can take 2,19,19 or 2,7,11 which for drawing purposes is equivalent to 1,1,2 and 2,7,9?

Discuss your decisions here!
also share any relevant details about your decisions if you want

UNR -> Nevada
St Anselm -> New Hampshire
PSU -> Pennsylvania
WCU -> North Carolina


Put your USERNAME in the list ONLY IF YOU WANT TO!!!! !!!!!

I'm going to UNR if anyone wants to meetup!!! :D

Current List:
Iowa
UNR
PSU
St Anselm
WCU

Hi everyone,

I am a current 11th grader living in Orange, Texas. I recently started doing competition math and I think I am pretty good at it. Recently I did a mock AMC8 and achieved a score of 21/25, which falls in the top 1% DHR. I also talked to my math teacher and she says I am an above average student.

Given my natural talent and the fact that I am willing to work ~3.5 hours a week studying competition math, do you think I will be able to make IMO next year? I am aware of the difficulty of this task but my mom says that I can achieve whatever I put my mind to, as long as I work hard.

Here is my plan for the next few months:

month 1-2: finish studying pre-algebra and learn geometry
month 3-4: learn pre-calculus
month 5-6: start doing IMO shortlist problems
month 7+: keep doing ISL/IMO problems.

Is this a feasible task? I am a girl btw.

The answer posted on the AOPS page for the 2022 AIME II problem 5 has some flaw in it and the final answer is incorrect.

The answer is trying to use the symmetric property for the a, b, c. However the numbers are not exactly cyclically symmetric in the problem.

For example, the solution works well with a = 20, it derives 4 different pairs of b and c for p2 is in (3, 5, 11, 17) as stated. However, for a = 19, only 3 p2 in the set works, since if the p2 = 17, we will have c = 0, which is not a possible vertex label. So only three pairs of b and c work for a= 19, which are (19, 17, 14), (19, 17, 12), (19, 17, 6).

Same for a = 18.

However, for a = 17, one more possibility joined. c can be bigger than a. So the total triple satisfying the problem is back to 4.

There are two more cases that the total number of working pairs of b, c is 3, when a = 5, and a = 4.

So the final answer for this problem is not 072. It should be 068.

Does anyone know where to find lists of USAMO medalists from past years? I can find the 2025 list on their website, but they don't seem to keep lists from previous years and I can't find it anywhere else. Thanks!

Hey! I got accepted into Ross Indiana, and I think I'll probably also get accepted into HCSSiM. I've been looking between the two camps, and I'm trying to decide which one to go to -- both seem like really fun options.

Instead of trying to explain my personal preferences and thought processes, I thought it might be a good idea to ask the community for their personal opinions on these camps. What are some things that you like or dislike about both camps? (Whether it be through personal experience or by word-of-mouth, but please specify if it's just something you've heard)

This will probably help me be more informed on making a final decision, so I'd appreciate any advice. Thanks in advance!

Hi everyone,
I just have a question. I live in PA and I sadly didn't make it to nationals this year. Is PA a competitive state? I'm new into mathcounts and not sure

Hi guys, I wanted to try out physics, this year I got a 14 on the f=ma and missed the usahpo cutoff by 1 point. But I am pretty bad at physics so I wanted to do a class to get better, I was wondering like what books or classes I should take, do you guys think physwoot would be a good fit? Would I struggle too much?