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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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line AO passes through the midpoint of segment EF
toanrathay   1
N 2 hours ago by joeym2011
Given a triangle \( ABC \) with \( AB < AC \) and the angle bisector \( AD \).
The line passing through \( A \) and perpendicular to \( AC \) intersects the line passing through \( B \) and parallel to \( AD \) at point \( E \).
The line passing through \( A \) and perpendicular to \( AB \) intersects the line passing through \( C \) and parallel to \( AD \) at point \( F \).
Let \( O \) be the intersection of the three perpendicular bisectors of triangle \( ABC \).
Prove that line \( AO \) passes through the midpoint of segment \( EF \).
1 reply
toanrathay
Today at 5:08 AM
joeym2011
2 hours ago
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Inequalities
sqing   13
N 2 hours ago by giangtruong13
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 $a=b=\frac{25}{66},c=\frac{8}{33}.$
13 replies
sqing
Mar 26, 2025
giangtruong13
2 hours ago
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inequality
sunshine_12   2
N 2 hours ago by sunshine_12
|a| + |b| + |c| − |a + b| − |b + c| − |c + a| + |a + b + c| ≥ 0
hey everyone, so I came across this inequality, and I did make some progress:
Let (a+b), (b+c), (c+a) be three sums T1, T2 and T3. As there are 3 sums, but they can be of only 2 signs, by pigeon hole principle, atleast 2 of the 3 sums must be of the same sign.
But I'm getting stuck on the case work. Can anyone help?
Thnx a lot
2 replies
sunshine_12
3 hours ago
sunshine_12
2 hours ago
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Inequalities from SXTX
sqing   12
N 3 hours ago by sqing
T702. Let $ a,b,c>0 $ and $ a+2b+3c=\sqrt{13}. $ Prove that $$ \sqrt{a^2+1} +2\sqrt{b^2+1} +3\sqrt{c^2+1} \geq 7$$S
T703. Let $ a,b $ be real numbers such that $ a+b\neq 0. $. Find the minimum of $ a^2+b^2+(\frac{1-ab}{a+b} )^2.$
T704. Let $ a,b,c>0 $ and $ a+b+c=3. $ Prove that $$ \frac{a^2+7}{(c+a)(a+b)} + \frac{b^2+7}{(a+b)(b+c)} +\frac{c^2+7}{(b+c)(c+a)} \geq 6$$S
12 replies
sqing
Feb 18, 2025
sqing
3 hours ago
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No more topics!
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Girls in Math at Yale 2025 Team P12:tangent circles
Bluesoul   4
N Mar 26, 2025 by Bluesoul
Consider triangle $ABC$ with $AB=5, BC=7, AC=8$. Denote the incircle of $\triangle{ABC}$ as $\omega$ and let $\omega$ meet $AB,AC,BC$ at $D,E,F$ respectively. Draw circle $\gamma$ such that $\gamma$ passes through $A$ and tangents to $BC$ at $F$. Denote the intersections of line $DE$ and $\gamma$ as $X$ and $Y$, the length of $XY$ can be written in the simplest form of $\frac{p\sqrt{q}}{r}$, compute $p+q+r$.
4 replies
Bluesoul
Mar 26, 2025
Bluesoul
Mar 26, 2025
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Girls in Math at Yale 2025 Team P12:tangent circles
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Reveal topic tags
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Bluesoul
878 posts
Bluesoul
#1 h  Mar 26, 2025, 8:49 AM
Y by
Consider triangle $ABC$ with $AB=5, BC=7, AC=8$. Denote the incircle of $\triangle{ABC}$ as $\omega$ and let $\omega$ meet $AB,AC,BC$ at $D,E,F$ respectively. Draw circle $\gamma$ such that $\gamma$ passes through $A$ and tangents to $BC$ at $F$. Denote the intersections of line $DE$ and $\gamma$ as $X$ and $Y$, the length of $XY$ can be written in the simplest form of $\frac{p\sqrt{q}}{r}$, compute $p+q+r$.
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Bluesoul
878 posts
Bluesoul
#2 h  Mar 26, 2025, 8:58 AM • 1 Y
Y by Rounak_iitr
This is my problem and I heard no team got it right in contest(in both USA and China) :love:

backstory
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ehuseyinyigit
793 posts
ehuseyinyigit
#3 h  Mar 26, 2025, 11:28 AM • 1 Y
Y by Bluesoul
The answer is $\boxed{114}$

Let $\gamma$ cut $AB$ and $AC$ at $Q_1$ and $Q_2$. Triangle $ADE$ is equilateral thus $DE=3$. Use PoP $BF^2=4=5BQ_1$ gives $BQ_1=4/5$. Similarly $CQ_2=25/8$. Since $AD=AE$, we obtain $Q_1D=6/5$ and $Q_2E=15/8$. Let $XD=x$ and $EY=y$. Then PoP gives $x(y+3)=3.6/5$ and $y(x+3)=3.15/8$. Thus, $y=x+27/40$. Plugging this value in PoP equations gives $x=\dfrac{-147+33\sqrt{41}}{80}$ and $XY=x+y+3=2x+147/40=\dfrac{33\sqrt{41}}{40}$. Then the answer is $\boxed{\dfrac{33\sqrt{41}}{40}}$.
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ehuseyinyigit
793 posts
ehuseyinyigit
#4 h  Mar 26, 2025, 3:26 PM
Y by
By tw nice problem, just as an AIME problem.
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Bluesoul
878 posts
Bluesoul
#5 h  Mar 26, 2025, 10:03 PM • 1 Y
Y by ehuseyinyigit
Your solution is the same as my first solution; but later I realized some alg manip can be made so we don't have to really solve the long quadratics

solution
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