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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following upcoming events:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
4th grader qual JMO
HCM2001   26
N a minute ago by lele0305
i mean.. whattttt??? just found out about this.. is he on aops? (i'm sure he is) where are you orz lol..
https://www.mathschool.com/blog/results/celebrating-success-douglas-zhang-is-rsm-s-youngest-usajmo-qualifier
26 replies
HCM2001
Yesterday at 12:53 AM
lele0305
a minute ago
Proof-based math
imbadatmath1233   4
N 2 hours ago by imbadatmath1233
Okay, I need help in deciding on how i am going to prep. My JMO index was 121.5+11 = 231.5(10A) and I missed the cutoff by 1.5. Ive already grieved about this before but I need some help in deciding what I should do next year. I think I can make JMO but my goal is to get 21+ on JMO. However, OTIS applications are already done so does anyone have any other tips on how to prep for JMO. Any help would be very much appreciated. Also, how much time should i spend on computational if i want to prep for olympiad but I don't want to get rusty. Thanks for helping!
4 replies
imbadatmath1233
4 hours ago
imbadatmath1233
2 hours ago
Awesome Math Rec Letter
cowstalker   0
2 hours ago
Hello, I recently looked at the MIT Primes website and saw that they accept recommendation letters from the Awesome Math Summer Program. Has anyone ever gotten a recommendation letter from one of the teachers in Awesome Math? I'm also planning to take AMSP and would like to get a rec letter from my teacher, too, so I was wondering if this is even possible or not.
0 replies
cowstalker
2 hours ago
0 replies
9 USAMO/JMO
BAM10   21
N 4 hours ago by imbadatmath1233
I mock ~90-100 on very recent AMC 10 mock right now. I plan to take AMC 10 final fives(9th), intermediate NT(9th), aime A+B courses in 10th and 11th and maybe mathWOOT 1 (12th). For more info I got 20 on this years AMC 8 with 3 sillies and 32 on MATHCOUNTS chapter. Also what is a realistic timeline to do this
21 replies
BAM10
May 19, 2025
imbadatmath1233
4 hours ago
No more topics!
apparently circles have two intersections :'(
itised   76
N Mar 16, 2025 by Ilikeminecraft
Source: 2020 USOJMO Problem 2
Let $\omega$ be the incircle of a fixed equilateral triangle $ABC$. Let $\ell$ be a variable line that is tangent to $\omega$ and meets the interior of segments $BC$ and $CA$ at points $P$ and $Q$, respectively. A point $R$ is chosen such that $PR = PA$ and $QR = QB$. Find all possible locations of the point $R$, over all choices of $\ell$.

Proposed by Titu Andreescu and Waldemar Pompe
76 replies
itised
Jun 21, 2020
Ilikeminecraft
Mar 16, 2025
apparently circles have two intersections :'(
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Source: 2020 USOJMO Problem 2
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itised
1720 posts
#1 • 5 Y
Y by samrocksnature, megarnie, HWenslawski, son7, Mango247
Let $\omega$ be the incircle of a fixed equilateral triangle $ABC$. Let $\ell$ be a variable line that is tangent to $\omega$ and meets the interior of segments $BC$ and $CA$ at points $P$ and $Q$, respectively. A point $R$ is chosen such that $PR = PA$ and $QR = QB$. Find all possible locations of the point $R$, over all choices of $\ell$.

Proposed by Titu Andreescu and Waldemar Pompe
This post has been edited 2 times. Last edited by djmathman, Jun 22, 2020, 5:29 AM
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alifenix-
1547 posts
#2 • 35 Y
Y by Twistya, yayups, barry.yyc, OlympusHero, wu2481632, AmirKhusrau, thedoge, Toinfinity, cw357, crazyeyemoody907, v4913, ilovepizza2020, HamstPan38825, centslordm, samrocksnature, tigerzhang, megarnie, Geometry285, OliverA, HWenslawski, math31415926535, son7, Zorger74, AwesomeYRY, suvamkonar, rayfish, EpicBird08, Turtwig113, Sedro, Marcus_Zhang, vrondoS, bjump, Alex-131, aidan0626, AlexWin0806
Circles have two intersections... :(
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Twistya
84 posts
#3 • 4 Y
Y by vvluo, samrocksnature, megarnie, son7
*cires* I feel your pain alifenix
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flashsonic
139 posts
#4 • 16 Y
Y by AZAZ12345, vvluo, OlympusHero, Kagebaka, couplefire, thedoge, pretzel, Lcz, centslordm, samrocksnature, megarnie, OliverA, son7, abeot, Marcus_Zhang, endless_abyss
I can't be the only one who misread PR=RA, QR=RB for the entirety of the test...
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KillerOrca2015
219 posts
#5 • 1 Y
Y by samrocksnature
the solution set for this problem was wacky
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jj_ca888
2726 posts
#6 • 1 Y
Y by samrocksnature
alifenix- wrote:
Circles have two intersections... :(

same
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Emathmaster
1911 posts
#7 • 1 Y
Y by samrocksnature
Outline

Nice problem but did not get this during the test.
This post has been edited 1 time. Last edited by Emathmaster, Jun 21, 2020, 11:04 PM
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dchenmathcounts
2443 posts
#8 • 5 Y
Y by cw357, samrocksnature, Mango247, Mango247, Mango247
flashsonic wrote:
I can't be the only one who misread PR=RA, QR=RB for the entirety of the test...

No. You were not.
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Gogobao
1039 posts
#9 • 4 Y
Y by samrocksnature, Mango247, Mango247, Mango247
I also did that and was wondering why the locus wasn't nice...
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Emathmaster
1911 posts
#10 • 1 Y
Y by samrocksnature
dchenmathcounts wrote:
flashsonic wrote:
I can't be the only one who misread PR=RA, QR=RB for the entirety of the test...

No. You were not.

I misread at first too.
This post has been edited 1 time. Last edited by Emathmaster, Jun 21, 2020, 11:05 PM
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Frestho
1100 posts
#11 • 3 Y
Y by myh2910, samrocksnature, Marcus_Zhang
3 liner
This post has been edited 2 times. Last edited by Frestho, Jun 22, 2020, 5:57 AM
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amuthup
779 posts
#12 • 1 Y
Y by samrocksnature
I can't be the only one who didn't see the equilateral until staring at the problem for an hour...
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sungs
108 posts
#13 • 1 Y
Y by samrocksnature
Say the incircle is tangent to BC, AC at A', B'. Dilate arc A'B' with respect to the incenter by magnitudes -2 and 4. Those new arcs are the answers
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ilovepi3.14
1443 posts
#14 • 1 Y
Y by samrocksnature
I centered circles at $A$ and $B$ instead of $P$ and $R$ for a very long time -_-.
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Awesome_guy
862 posts
#15 • 1 Y
Y by samrocksnature
Let each $R$ be split into $R_1$ and $R_2$. The crux of the problem is prove the incenter lies on $R_1R_2$ by perpendicularity lemma. Then proceed to length chase.
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