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k a My Retirement & New Leadership at AoPS
rrusczyk   1571
N Mar 26, 2025 by SmartGroot
I write today to announce my retirement as CEO from Art of Problem Solving. When I founded AoPS 22 years ago, I never imagined that we would reach so many students and families, or that we would find so many channels through which we discover, inspire, and train the great problem solvers of the next generation. I am very proud of all we have accomplished and I’m thankful for the many supporters who provided inspiration and encouragement along the way. I'm particularly grateful to all of the wonderful members of the AoPS Community!

I’m delighted to introduce our new leaders - Ben Kornell and Andrew Sutherland. Ben has extensive experience in education and edtech prior to joining AoPS as my successor as CEO, including starting like I did as a classroom teacher. He has a deep understanding of the value of our work because he’s an AoPS parent! Meanwhile, Andrew and I have common roots as founders of education companies; he launched Quizlet at age 15! His journey from founder to MIT to technology and product leader as our Chief Product Officer traces a pathway many of our students will follow in the years to come.

Thank you again for your support for Art of Problem Solving and we look forward to working with millions more wonderful problem solvers in the years to come.

And special thanks to all of the amazing AoPS team members who have helped build AoPS. We’ve come a long way from here:IMAGE
1571 replies
rrusczyk
Mar 24, 2025
SmartGroot
Mar 26, 2025
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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
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Geometry Ratio
steven_zhang123   0
4 minutes ago
Source: 0
In triangle \( \triangle PQR \), \( PQ = PR \), and \( \angle P = 120^\circ \). Points \( M \) and \( N \) are located on \( PQ \) and \( PR \) respectively, such that \( PQ = 2 \cdot PM \) and \( \angle PMN = \angle NQR \). Find the ratio of \( PN \) to \( NR \).
0 replies
steven_zhang123
4 minutes ago
0 replies
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IMO Shortlist 2013, Geometry #2
lyukhson   78
N 7 minutes ago by numbertheory97
Source: IMO Shortlist 2013, Geometry #2
Let $\omega$ be the circumcircle of a triangle $ABC$. Denote by $M$ and $N$ the midpoints of the sides $AB$ and $AC$, respectively, and denote by $T$ the midpoint of the arc $BC$ of $\omega$ not containing $A$. The circumcircles of the triangles $AMT$ and $ANT$ intersect the perpendicular bisectors of $AC$ and $AB$ at points $X$ and $Y$, respectively; assume that $X$ and $Y$ lie inside the triangle $ABC$. The lines $MN$ and $XY$ intersect at $K$. Prove that $KA=KT$.
78 replies
1 viewing
lyukhson
Jul 9, 2014
numbertheory97
7 minutes ago
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Romania TST 2021 Day 1 P4
oVlad   21
N 10 minutes ago by ravengsd
Determine all functions $f:\mathbb{R}\to\mathbb{R}$ which satisfy the following relationship for all real numbers $x$ and $y$\[f(xf(y)-f(x))=2f(x)+xy.\]
21 replies
oVlad
May 15, 2021
ravengsd
10 minutes ago
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geometry
Duc15_g-yh   2
N 17 minutes ago by Duc15_g-yh
Source: Original
Title: Geometry Problem – Equal Angles and Concurrency

Post Content:

Hi everyone,

I need help solving this geometry problem:

Given a triangle ABC, let (C_1) be the excircle touching BC, CA, AB at X, P, Q respectively. Similarly, let (C_2) be the excircle touching CA, AB, BC at Y, M, N respectively.
1. Prove that \angle YMN = \angle XQP.
2. Let S be the intersection of MN and PQ. Prove that MY, PX, and SC are concurrent.

Any hints or full solutions would be greatly appreciated!

Thanks in advance!
2 replies
Duc15_g-yh
27 minutes ago
Duc15_g-yh
17 minutes ago
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Solve the equetion
yt12   3
N an hour ago by rchokler
Solve the equetion:$\sin 2x+\tan x=2$
3 replies
yt12
Today at 8:34 AM
rchokler
an hour ago
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An inequality
JK1603JK   0
2 hours ago
Let a,b,c\ge 0: a+b+c>0 then prove \frac{a^{2}-bc}{3a+b+c}+\frac{b^{2}-ca}{3b+c+a}+\frac{c^{2}-ab}{3c+a+b}\ge 0
0 replies
JK1603JK
2 hours ago
0 replies
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Inequality
lgx57   1
N 2 hours ago by sqing
Let $x,y,z \ge 0$ and $xyz=1$. Prove that

$$\sum \frac{1}{x^2+x+1} \ge 1$$
1 reply
lgx57
2 hours ago
sqing
2 hours ago
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Inequalities
sqing   0
3 hours ago
Let $ a,b,c> 0 $ and $ab+bc+ca+abc =4. $ Prove that
$$ \frac{3 }{ a+b+c}+\frac{1}{abc} \geq2$$$$\frac{37 }{ a+b+c}+\frac{10}{abc} \geq\frac{67}{3}$$
0 replies
sqing
3 hours ago
0 replies
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Inequalities
sqing   22
N 4 hours ago by sqing
Let $ a,b,c\geq 0 $ and $a+b+c=1$. Prove that
$$a^2+b^2+ ab +21abc\leq\frac{512}{441}$$Equality holds when $a=b=\frac{38}{21},c=\frac{5}{214}.$
$$a^2+b^2+ ab +19abc\leq\frac{10648}{9747}$$Equality holds when $a=b=\frac{22}{57},c=\frac{13}{57}.$
$$a^2+b^2+ ab +22abc\leq\frac{15625}{13068}$$Equality holds when $a=b=\frac{25}{66},c=\frac{8}{33}.$
22 replies
sqing
Mar 26, 2025
sqing
4 hours ago
J
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An inequality
JK1603JK   1
N Today at 9:27 AM by lbh_qys
Let a,b,c\ge 0: ab+bc+ca>0 then prove \frac{4ab+5c^2}{a+b}+\frac{4bc+5a^2}{b+c}+\frac{4ca+5b^2}{c+a}\ge \frac{3}{2}\cdot\frac{(a+b+c)^3}{ab+bc+ca}.
1 reply
JK1603JK
Today at 7:11 AM
lbh_qys
Today at 9:27 AM
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functional equation in R2
jasperE3   2
N Today at 9:14 AM by alexheinis
Find all functions $f:\mathbb R\times\mathbb R\to\mathbb R$ such that:
$a)\enspace f(x+z,y+z)=f(x,y)+z$
$b)\enspace f(xw,yw)=wf(x,y)$
both hold $\forall w,x,y,z\in\mathbb R,w\ne0$.
2 replies
jasperE3
Mar 27, 2021
alexheinis
Today at 9:14 AM
J
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inequality
JK1603JK   3
N Today at 8:03 AM by lbh_qys
Let a,b,c\ge 0: ab+bc+ca>0 then prove \frac{3a-b-c}{b^2+c^2}+\frac{3b-c-a}{c^2+a^2}+\frac{3c-a-b}{a^2+b^2}\ge \frac{3}{2}\cdot\frac{a+b+c}{ab+bc+ca}
3 replies
JK1603JK
Mar 29, 2025
lbh_qys
Today at 8:03 AM
J
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Functional Equation
ab_xy123   3
N Today at 6:30 AM by jasperE3
Find all solutions to the functional equation $f(1-x) = f(x) + 1 - 2x$
3 replies
ab_xy123
Mar 16, 2020
jasperE3
Today at 6:30 AM
J
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Trivial Functional Equation
OlympusHero   8
N Today at 6:21 AM by jasperE3
For all functions $f: \mathbb{R}\rightarrow \mathbb{R}$, solve the functional equation $f(f(n))+f(n)=2$.
8 replies
OlympusHero
May 10, 2021
jasperE3
Today at 6:21 AM
J
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J
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EGMO Genre Predictions
ohiorizzler1434   14
N Mar 28, 2025 by amburger
Everybody, with EGMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
14 replies
ohiorizzler1434
Mar 28, 2025
amburger
Mar 28, 2025
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EGMO Genre Predictions
G H J
Reveal topic tags
EGMO
L
G H BBookmark kLocked kLocked NReply
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ohiorizzler1434
745 posts
ohiorizzler1434
#1 h  Mar 28, 2025, 4:16 AM • 1 Y
Y by OronSH
Everybody, with EGMO upcoming, what are you predictions for the problem genres?


Personally I predict: predict
Z K Y
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sixoneeight
1135 posts
sixoneeight
#2 h  Mar 28, 2025, 4:36 AM
Y by
CAG AGC (no N of course)
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Haris1
67 posts
Haris1
#3 h  Mar 28, 2025, 8:54 AM • 1 Y
Y by Sadigly
AAA GGG trust triple fe incoming with length geos in day 2. :ninja:
Z K Y
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BR1F1SZ
544 posts
BR1F1SZ
#4 h  Mar 28, 2025, 10:07 AM
Y by
Do the IMO rules apply? (i.e. must problems $1$, $2$, $4$, $5$ be different subjects?)
This post has been edited 1 time. Last edited by BR1F1SZ, Mar 28, 2025, 10:07 AM
Z K Y
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alexanderhamilton124
381 posts
alexanderhamilton124
#5 h  Mar 28, 2025, 10:58 AM
Y by
im not sure @above

im hoping for ANGNCA
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BR1F1SZ
544 posts
BR1F1SZ
#6 h  Mar 28, 2025, 11:00 AM
Y by
BR1F1SZ wrote:
Do the IMO rules apply? (i.e. must problems $1$, $2$, $4$, $5$ be different subjects?)

I guess NCG GAC
Z K Y
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NicoN9
85 posts
NicoN9
#7 h  Mar 28, 2025, 11:15 AM
Y by
I guess GAN CNG
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maths_enthusiast_0001
131 posts
maths_enthusiast_0001
#8 h  Mar 28, 2025, 11:21 AM
Y by
GGG GGG
:ddr: :gathering:
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GreekIdiot
151 posts
GreekIdiot
#9 h  Mar 28, 2025, 2:40 PM
Y by
CCC CCC
:whistling:
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ItsBesi
139 posts
ItsBesi
#10 h  Mar 28, 2025, 3:21 PM
Y by
Happy that EGMO will be organised on my country (KOSOVO) I hope it's going to be:GCA NAG :play_ball:
This post has been edited 1 time. Last edited by ItsBesi, Mar 28, 2025, 7:15 PM
Z K Y
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bjump
994 posts
bjump
#11 h  Mar 28, 2025, 3:37 PM
Y by
CNA ACN

Geometry is dead :(
Z K Y
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Jupiterballs
33 posts
Jupiterballs
#12 h  Mar 28, 2025, 3:41 PM
Y by
Hmm, maybe AGC ANG
Z K Y
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Primeniyazidayi
30 posts
Primeniyazidayi
#13 h  Mar 28, 2025, 3:51 PM
Y by
I hope GCA GNA. At least I can solve geos and pretend that I'm good at geo:)
This post has been edited 1 time. Last edited by Primeniyazidayi, Mar 28, 2025, 3:52 PM
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amburger
5 posts
amburger
#14 h  Mar 28, 2025, 9:41 PM
Y by
imagine if they pull up with a p3 level A like last yr;s p6
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amburger
5 posts
amburger
#15 h  Mar 28, 2025, 9:41 PM
Y by
oh god i hope as little A as possible egmo A tends to be so bashy

2024 p5 was so bad
This post has been edited 1 time. Last edited by amburger, Mar 28, 2025, 9:44 PM
Reason: f
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