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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. 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 events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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0 replies
jlacosta
Apr 2, 2025
0 replies
k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
MathPath
PatTheKing806   5
N 34 minutes ago by eyzMath
Is anybody else going to MathPath?

I haven't gotten in. its been 3+ weeks since they said my application was done.
5 replies
PatTheKing806
Mar 24, 2025
eyzMath
34 minutes ago
MOP Emails
hellohannah   99
N 36 minutes ago by CatCatHead
So mop emails are probably coming tomorrow, feel free to discuss here. I'll probably post when I hear that they're out unless I'm asleep
99 replies
+1 w
hellohannah
Yesterday at 4:59 AM
CatCatHead
36 minutes ago
AMC and JMO qual question
HungryCalculator   4
N 36 minutes ago by eyzMath
Say that on the AMC 10, you do better on the A than the B, but you still qualify for AIME thru both. Then after your AIME, it turns out that you didn’t make JMO through the A+AIME index but you did pass the threshold for the B+AIME index.

does MAA consider your B+AIME index over the A+AIME index and consider you a JMO qualifier even tho Your A test score was higher?

4 replies
HungryCalculator
Apr 17, 2025
eyzMath
36 minutes ago
2025 Math and AI 4 Girls Competition: Win Up To $1,000!!!
audio-on   55
N 40 minutes ago by eyzMath
Join the 2025 Math and AI 4 Girls Competition for a chance to win up to $1,000!

Hey Everyone, I'm pleased to announce the dates for the 2025 MA4G Competition are set!
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (@ 11:59pm PST).

Applicants will have one month to fill out an application with prizes for the top 50 contestants & cash prizes for the top 20 contestants (including $1,000 for the winner!). More details below!

Eligibility:
The competition is free to enter, and open to middle school female students living in the US (5th-8th grade).
Award recipients are selected based on their aptitude, activities and aspirations in STEM.

Event dates:
Applications will open on March 22nd, 2025, and they will close on April 26th, 2025 (by 11:59pm PST)
Winners will be announced on June 28, 2025 during an online award ceremony.

Application requirements:
Complete a 12 question problem set on math and computer science/AI related topics
Write 2 short essays

Prizes:
1st place: $1,000 Cash prize
2nd place: $500 Cash prize
3rd place: $300 Cash prize
4th-10th: $100 Cash prize each
11th-20th: $50 Cash prize each
Top 50 contestants: Over $50 worth of gadgets and stationary


Many thanks to our current and past sponsors and partners: Hudson River Trading, MATHCOUNTS, Hewlett Packard Enterprise, Automation Anywhere, JP Morgan Chase, D.E. Shaw, and AI4ALL.

Math and AI 4 Girls is a nonprofit organization aiming to encourage young girls to develop an interest in math and AI by taking part in STEM competitions and activities at an early age. The organization will be hosting an inaugural Math and AI 4 Girls competition to identify talent and encourage long-term planning of academic and career goals in STEM.

Contact:
mathandAI4girls@yahoo.com

For more information on the competition:
https://www.mathandai4girls.org/math-and-ai-4-girls-competition

More information on how to register will be posted on the website. If you have any questions, please ask here!


55 replies
audio-on
Jan 26, 2025
eyzMath
40 minutes ago
Medium geometry with AH diameter circle
v_Enhance   93
N Yesterday at 10:36 AM by waterbottle432
Source: USA TSTST 2016 Problem 2, by Evan Chen
Let $ABC$ be a scalene triangle with orthocenter $H$ and circumcenter $O$. Denote by $M$, $N$ the midpoints of $\overline{AH}$, $\overline{BC}$. Suppose the circle $\gamma$ with diameter $\overline{AH}$ meets the circumcircle of $ABC$ at $G \neq A$, and meets line $AN$ at a point $Q \neq A$. The tangent to $\gamma$ at $G$ meets line $OM$ at $P$. Show that the circumcircles of $\triangle GNQ$ and $\triangle MBC$ intersect at a point $T$ on $\overline{PN}$.

Proposed by Evan Chen
93 replies
v_Enhance
Jun 28, 2016
waterbottle432
Yesterday at 10:36 AM
Reflected point lies on radical axis
Mahdi_Mashayekhi   3
N Apr 19, 2025 by Mahdi_Mashayekhi
Source: Iran 2025 second round P4
Given is an acute and scalene triangle $ABC$ with circumcenter $O$. $BO$ and $CO$ intersect the altitude from $A$ to $BC$ at points $P$ and $Q$ respectively. $X$ is the circumcenter of triangle $OPQ$ and $O'$ is the reflection of $O$ over $BC$. $Y$ is the second intersection of circumcircles of triangles $BXP$ and $CXQ$. Show that $X,Y,O'$ are collinear.
3 replies
Mahdi_Mashayekhi
Apr 19, 2025
Mahdi_Mashayekhi
Apr 19, 2025
A mediane as a radical axis
breloje17fr   0
Apr 19, 2025
Hello, ladies and gentlemen
Let ABC be a triangle, and D, E and F the middles of the sides BC, CA and AB respectively. The perpendicular bissector of CA intersects the line AB at E' and the bissector of the A angle at K, and the perpendicular bissector of AB intersects the line AC at F' and the bissector of the A angle at J. The two circles passing through J, F and E' and through K, E and F' intersect each other at P and Q.
Show that the radical axis of these circles is the A-mediane of ABC.
0 replies
breloje17fr
Apr 19, 2025
0 replies
Concurrence in Cyclic Quadrilateral
GrantStar   38
N Apr 17, 2025 by wu2481632
Source: IMO Shortlist 2023 G3
Let $ABCD$ be a cyclic quadrilateral with $\angle BAD < \angle ADC$. Let $M$ be the midpoint of the arc $CD$ not containing $A$. Suppose there is a point $P$ inside $ABCD$ such that $\angle ADB = \angle CPD$ and $\angle ADP = \angle PCB$.

Prove that lines $AD, PM$, and $BC$ are concurrent.
38 replies
GrantStar
Jul 17, 2024
wu2481632
Apr 17, 2025
Circles with same radical axis
Jalil_Huseynov   9
N Apr 17, 2025 by Nari_Tom
Source: DGO 2021, Individual stage, Day2 P3
Let $O$ be the circumcenter of triangle $ABC$. The altitudes from $A, B, C$ of triangle $ABC$ intersects the circumcircle of the triangle $ABC$ at $A_1, B_1, C_1$ respectively. $AO, BO, CO$ meets $BC, CA, AB$ at $A_2, B_2, C_2$ respectively. Prove that the circumcircles of triangles $AA_1A_2, BB_1B_2, CC_1C_2$ share two common points.

Proporsed by wassupevery1
9 replies
Jalil_Huseynov
Dec 26, 2021
Nari_Tom
Apr 17, 2025
2011 Japan Mathematical Olympiad Finals Problem 1
Kunihiko_Chikaya   20
N Apr 14, 2025 by zhoujef000
Source: Japanese MO Finals 2011
Given an acute triangle $ABC$ with the midpoint $M$ of $BC$. Draw the perpendicular $HP$ from the orthocenter $H$ of $ABC$ to $AM$.
Show that $AM\cdot PM=BM^2$.
20 replies
Kunihiko_Chikaya
Feb 11, 2011
zhoujef000
Apr 14, 2025
IMO 2008, Question 1
orl   154
N Apr 8, 2025 by eg4334
Source: IMO Shortlist 2008, G1
Let $ H$ be the orthocenter of an acute-angled triangle $ ABC$. The circle $ \Gamma_{A}$ centered at the midpoint of $ BC$ and passing through $ H$ intersects the sideline $ BC$ at points $ A_{1}$ and $ A_{2}$. Similarly, define the points $ B_{1}$, $ B_{2}$, $ C_{1}$ and $ C_{2}$.

Prove that the six points $ A_{1}$, $ A_{2}$, $ B_{1}$, $ B_{2}$, $ C_{1}$ and $ C_{2}$ are concyclic.

Author: Andrey Gavrilyuk, Russia
154 replies
orl
Jul 16, 2008
eg4334
Apr 8, 2025
Lines pass through a common point
April   4
N Apr 7, 2025 by Nari_Tom
Source: Baltic Way 2008, Problem 18
Let $ AB$ be a diameter of a circle $ S$, and let $ L$ be the tangent at $ A$. Furthermore, let $ c$ be a fixed, positive real, and consider all pairs of points $ X$ and $ Y$ lying on $ L$, on opposite sides of $ A$, such that $ |AX|\cdot |AY| = c$. The lines $ BX$ and $ BY$ intersect $ S$ at points $ P$ and $ Q$, respectively. Show that all the lines $ PQ$ pass through a common point.
4 replies
April
Nov 23, 2008
Nari_Tom
Apr 7, 2025
perpendicularity involving ex and incenter
Erken   19
N Apr 6, 2025 by Primeniyazidayi
Source: Kazakhstan NO 2008 problem 2
Suppose that $ B_1$ is the midpoint of the arc $ AC$, containing $ B$, in the circumcircle of $ \triangle ABC$, and let $ I_b$ be the $ B$-excircle's center. Assume that the external angle bisector of $ \angle ABC$ intersects $ AC$ at $ B_2$. Prove that $ B_2I$ is perpendicular to $ B_1I_B$, where $ I$ is the incenter of $ \triangle ABC$.
19 replies
Erken
Dec 24, 2008
Primeniyazidayi
Apr 6, 2025
Geo with unnecessary condition
egxa   8
N Apr 4, 2025 by ErTeeEs06
Source: Turkey Olympic Revenge 2024 P4
Let the circumcircle of a triangle $ABC$ be $\Gamma$. The tangents to $\Gamma$ at $B,C$ meet at point $E$. For a point $F$ on line $BC$ which is not on the segment $BC$, let the midpoint of $EF$ be $G$. Lines $GB,GC$ meet $\Gamma$ again at points $I,H$ respectively. Let $M$ be the midpoint of $BC$. Prove that the points $F,I,H,M$ lie on a circle.

Proposed by Mehmet Can Baştemir
8 replies
egxa
Aug 6, 2024
ErTeeEs06
Apr 4, 2025
MOP Qualification
tamjazad   7
N Sep 11, 2016 by v_Enhance
What would one have to make on the USA(J)MO to make mop?
7 replies
tamjazad
Sep 6, 2016
v_Enhance
Sep 11, 2016
MOP Qualification
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tamjazad
54 posts
#1 • 2 Y
Y by Adventure10, Mango247
What would one have to make on the USA(J)MO to make mop?
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Generic_Username
1088 posts
#2 • 2 Y
Y by Adventure10, Mango247
tamjazad wrote:
What would one have to make on the USA(J)MO to make mop?

You'd normally have to win the USA(J)MO, or in the case of last year, be a very high HM. You can see previous years' cutoff scores here.
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ayushk
362 posts
#3 • 2 Y
Y by Adventure10, Mango247
You can read about it here: http://artofproblemsolving.com/community/c5h1079745p4737466
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v_Enhance
6874 posts
#4 • 4 Y
Y by v4913, HamstPan38825, Adventure10, Mango247
From http://www.mit.edu/~evanchen/FAQs/rules.html, relevant excerpt bolded below
Quote:
Before I say anything I want to say that the criteria for MOP invitations are not especially well-defined. Each year, the exact number and choice of students is determined based on the exact scores for that year.

That being said, as of 2016 the criteria for MOP is roughly as follows:

IMO team members and alternates ("black" group)
The next approximately 12 non-graduating USAMO students ("blue" group).
The next approximately 12 USAMO students in 9th and 10th grades ("green" or "red")
The top approximately 12 students on USAJMO ("red" group)
Some varying number of non-graduating female contestants from either USAMO or USAJMO (these students represent USA at the European Girls' Math Olympiad). The exact cutoffs for each contest are determined based on the scores for that year.

Young students in 8th grades and below are invited to MOP if and only if the moon is full and the wind is blowing south-south-east. All selection is done by ID number, without student names.

The "color groups" are a convenient shorthand and not worth worrying about.
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stephcurry
2095 posts
#5 • 2 Y
Y by rafayaashary1, Adventure10
v_Enhance wrote:
Young students in 8th grades and below are invited to MOP if and only if the moon is full and the wind is blowing south-south-east. All selection is done by ID number, without student names.

Is this true? I've never heard this rule before ;)

Seriously though, they should make some sort of set rule for admitting people in 8th grade and below, as it seems highly subjective from year to year
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FiveMops03
6 posts
#6 • 2 Y
Y by Adventure10, Mango247
stephcurry wrote:
v_Enhance wrote:
Young students in 8th grades and below are invited to MOP if and only if the moon is full and the wind is blowing south-south-east. All selection is done by ID number, without student names.

Is this true? I've never heard this rule before ;)

Seriously though, they should make some sort of set rule for admitting people in 8th grade and below, as it seems highly subjective from year to year

Does it have anything to do with MATHCOUNTS? The three middle schoolers who made it this year were 1,2,S at countdown; 1, 2, 3 written. The next few highest scoring middle school JMO participants (the two other middle school winners, and one of the two middle school HMs) did not make MATHCOUNTS nationals. Moreover, the MOP invitations were personally given by Po-Shen at nationals (if I'm not mistaken).
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Wave-Particle
3690 posts
#7 • 5 Y
Y by budu, catpiano, rafayaashary1, Adventure10, Mango247
FiveMops03 wrote:
stephcurry wrote:
v_Enhance wrote:
Young students in 8th grades and below are invited to MOP if and only if the moon is full and the wind is blowing south-south-east. All selection is done by ID number, without student names.

Is this true? I've never heard this rule before ;)

Seriously though, they should make some sort of set rule for admitting people in 8th grade and below, as it seems highly subjective from year to year

Does it have anything to do with MATHCOUNTS? The three middle schoolers who made it this year were 1,2,S at countdown; 1, 2, 3 written. The next few highest scoring middle school JMO participants (the two other middle school winners, and one of the two middle school HMs) did not make MATHCOUNTS nationals. Moreover, the MOP invitations were personally given by Po-Shen at nationals (if I'm not mistaken).

No it doesn't have to do with MATHCOUNTS. These middle schoolers also scored higher than the other middle schoolers on the JMO/AMO which is why they were picked. Also, last year the middle school MOPper did not attend nationals which is more proof it has nothing to do with MATHCOUNTS.
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v_Enhance
6874 posts
#8 • 5 Y
Y by wu2481632, Wave-Particle, v4913, HamstPan38825, Adventure10
FiveMops03 wrote:
Does it have anything to do with MATHCOUNTS?
As I said already: all selection is done by ID number, without student names. Since we do not have Mathcounts scores attached to USA(J)MO ID numbers it is impossible for Mathcounts performance to affect the selection in any way.
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