[/quote]
,
(i dont remember exactly if it was 8032038 or some other number, so correct me on this)
(i posted this at 12:29) lol
?
and 
Prove that
,
,
,
are integers such that 
.
and 
of 
such that for each integer 
with 
,![\[ n\mid a_i - b_i - c_i
\]](http://latex.artofproblemsolving.com/1/a/e/1ae8d54f068b646ac7a1e43d75e7f26510cfdc95.png)
be an odd prime and 
be integers so that the integers 
are divisible by 
Prove that 
be real numbers such that 
Prove that 
Where 
be a triangle with circumcircle 
.
and 
respectively denote the midpoints of the arcs 
and 
that do not contain the third vertex. Let 
denote the midpoint of arc 
(the arc 
including 
)
be the incenter of 
be the circle that is tangent to 
be the circle that is tangent to 
,
friends, 
people are seated around a circular table in a fixed order. Ali places 
is the circumcenter of 
.
lie on 
,
is tangent to circumcircle of 
.
is tangent to circumcircle of triangle 
.
Y by Pengu14, Alex-131, miguel00, Skillfulcotton, Maximilian113, scannose, steven0531, Countmath1, Danielzh, pingpongmerrily, cubres, Exponent11, rayford, aidan0626
Hello everyone. I know this question may sound ridiculous/neagtive but I really want to know how the rest of the community thinks on this issue. Please excuse this yap session and feel free to ignore this post if it doesn't make sense, I don't think I really have a sane mind these days and something has gotten into my head.
I want your advice on what I should do in this situation. It has been my dream to make usamo since ~second semester of 9th grade and I started grinding from that time on. Last year, I qualified for the aime and got a 5. This year I really wanted to qualify for the olympiad and studied really hard. I spent my entire summer working on counting and probability, the subject I suck at the most. And yet, on amc 12, I fumbled hard. I usually mocked ~120-130s on amc 10s but on amc 12 this year, I got really mediocre scores ~100. So I had no chance of making usamo.
So during winter of 2024-2025 I kinda gave up on aime studying and I was like "hey, if I can't get into usamo, maybe ill qualify for usapho." Since I was pretty good at physics at that time. So I spended my winter hard grinding for f=ma and guess what? The test had stupid and ridiculous questions and I only got an 11. What really sucks is that even with the stupid amount of cheaters in f=ma, if I changed all of my "D" guesses to "C," then I would have qualified. Since I solved 10 actually and guessed the rest. Absolutely unfair that only 1 of my guesses were correct.
And also since I didn't study for aime, I ended up being super rusty and so I only got a 7. Solved 9 tho. (I usually can consistently solve 10+ on aimes).
And now here's my senior year and ofc I want to apply to a prestigious college. But it feels stupid that I don't have any usamo or usapho titles like the people I know do. I think I will have good essays primarily due to a varied amount of life experiences but like, I don't feel like I will contribute much to the college without being some prestigious olympiad qualifier. So this led to me having a self esteem issue.
This also led me to the question: should I study one last year so that I can get into usamo in my senior year, or is there no point? Since like, colleges don't care about whatever the hell you do in your senior year, and also, it seems just 'weird' to be grinding math contests while the rest of the people from my school are playing around, etc. So this time around I've really been having an internal crisis between my self esteem (since getting into usamo will raise my self esteem a lot) and college/senior choices.
I know this may seem like a dumb question to some and you are free to completely ignore the post. That's fine. I just really want advice for what I should do in this situation and it would really help bring my life quality up
Thanks,
hypotenuse
I want your advice on what I should do in this situation. It has been my dream to make usamo since ~second semester of 9th grade and I started grinding from that time on. Last year, I qualified for the aime and got a 5. This year I really wanted to qualify for the olympiad and studied really hard. I spent my entire summer working on counting and probability, the subject I suck at the most. And yet, on amc 12, I fumbled hard. I usually mocked ~120-130s on amc 10s but on amc 12 this year, I got really mediocre scores ~100. So I had no chance of making usamo.
So during winter of 2024-2025 I kinda gave up on aime studying and I was like "hey, if I can't get into usamo, maybe ill qualify for usapho." Since I was pretty good at physics at that time. So I spended my winter hard grinding for f=ma and guess what? The test had stupid and ridiculous questions and I only got an 11. What really sucks is that even with the stupid amount of cheaters in f=ma, if I changed all of my "D" guesses to "C," then I would have qualified. Since I solved 10 actually and guessed the rest. Absolutely unfair that only 1 of my guesses were correct.
And also since I didn't study for aime, I ended up being super rusty and so I only got a 7. Solved 9 tho. (I usually can consistently solve 10+ on aimes).
And now here's my senior year and ofc I want to apply to a prestigious college. But it feels stupid that I don't have any usamo or usapho titles like the people I know do. I think I will have good essays primarily due to a varied amount of life experiences but like, I don't feel like I will contribute much to the college without being some prestigious olympiad qualifier. So this led to me having a self esteem issue.
This also led me to the question: should I study one last year so that I can get into usamo in my senior year, or is there no point? Since like, colleges don't care about whatever the hell you do in your senior year, and also, it seems just 'weird' to be grinding math contests while the rest of the people from my school are playing around, etc. So this time around I've really been having an internal crisis between my self esteem (since getting into usamo will raise my self esteem a lot) and college/senior choices.
I know this may seem like a dumb question to some and you are free to completely ignore the post. That's fine. I just really want advice for what I should do in this situation and it would really help bring my life quality up
Thanks,
hypotenuse
