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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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Angles TXA and BAC are equal
nAalniaOMliO   1
N a minute ago by Retemoeg
Source: Belarusian National Olympiad 2025
Altitudes $BE$ and $CF$ of triangle $ABC$ intersect in $H$. A perpendicular $HT$ from $H$ to $EF$ is drawn. Circumcircles $ABC$ and $BHT$ intersect at $B$ and $X$.
Prove that $\angle TXA= \angle BAC$.
1 reply
nAalniaOMliO
Friday at 8:23 PM
Retemoeg
a minute ago
J
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GOTEEM #1: Incircle Concurrency
tworigami   30
N 2 minutes ago by ErTeeEs06
Source: GOTEEM: Mock Geometry Olympiad
Let $ABC$ be a scalene triangle. The incircle of $\triangle ABC$ is tangent to sides $\overline{BC}$, $\overline{CA}$, $\overline{AB}$ at $D, E, F$, respectively. Let $G$ be a point on the incircle of $\triangle ABC$ such that $\angle AGD = 90^\circ$. If lines $DG$ and $EF$ intersect at $P$, prove that $AP$ is parallel to $BC$.

Proposed by bluek
30 replies
tworigami
Jan 2, 2020
ErTeeEs06
2 minutes ago
J
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The Tetrahedral Space Partition
jannatiar   2
N 18 minutes ago by sami1618
Source: 2025 AlborzMO Day 2 P3
Is it possible to partition three-dimensional space into tetrahedra (not necessarily regular) such that there exists a plane that intersects the edges of each tetrahedron at exactly 4 or 0 points?

Proposed by Arvin Taheri
2 replies
jannatiar
Mar 9, 2025
sami1618
18 minutes ago
J
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A geometry problem
Lttgeometry   0
34 minutes ago
Given a non-isosceles triangle $ABC$ that is inscribed in $(O)$ . The incircle $(I)$ is tangent to $BC,CA,AB$ at $D,E,F$ respectively. A line through $A$ parallel to $BC$ intersects $(O)$ at $T$, and $TD$ intersects $(O)$ again at $J$. Let $N$ is the midpoint of $BC$. $P,Q$ be the second intersection of $JE,JF$ with $(O)$. $AI$ intersects $(O)$ again at $M$. Prove that the line passing through $A$ perpendicular to $PQ$ bisects $MN$.
0 replies
+1 w
Lttgeometry
34 minutes ago
0 replies
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No more topics!
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A simple and nice inequality in a triangle.
Virgil Nicula   7
N Jun 26, 2016 by Virgil Nicula
Source: Own (?)
I don't meet this inequality until today ...

PP. Let $ABC$ be a triangle with the angled-bisectors $BE$ , $CF$ where $E\in AC$ , $F\in AB\ .$ Prove that $\boxed{\ EF^2\ \le\ BF\cdot CE\ }\ (*)\ .$
7 replies
Virgil Nicula
May 19, 2016
Virgil Nicula
Jun 26, 2016
J
A simple and nice inequality in a triangle.
G H J
Reveal topic tags
inequalities
geometry
L
G H BBookmark kLocked kLocked NReply
Source: Own (?)
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Virgil Nicula
7054 posts
Virgil Nicula
#1 h  May 19, 2016, 4:52 PM • 2 Y
Y by Adventure10, Mango247
I don't meet this inequality until today ...

PP. Let $ABC$ be a triangle with the angled-bisectors $BE$ , $CF$ where $E\in AC$ , $F\in AB\ .$ Prove that $\boxed{\ EF^2\ \le\ BF\cdot CE\ }\ (*)\ .$
Z K Y
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arqady
30161 posts
arqady
#2 h  May 19, 2016, 7:33 PM • 2 Y
Y by Adventure10, Mango247
Indeed, it's $(b-c)^2a(a+b+c)\geq0$.
Z K Y
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aopser123
136 posts
aopser123
#3 h  May 19, 2016, 7:49 PM • 2 Y
Y by Adventure10, Mango247
arqady wrote:
Indeed, it's $(b-c)^2a(a+b+c)\geq0$.

How did you get this?
Z K Y
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Virgil Nicula
7054 posts
Virgil Nicula
#4 h  May 19, 2016, 8:38 PM • 2 Y
Y by Adventure10, Mango247
arqady wrote:
Indeed, it's $(b-c)^2a(a+b+c)\geq0$.

Yes, it is and my conclusion. See proposed problem P6 from here. Please, met you at least once this inequality ?! Thank you.
This post has been edited 2 times. Last edited by Virgil Nicula, May 20, 2016, 12:57 AM
Z K Y
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arqady
30161 posts
arqady
#5 h  May 19, 2016, 10:35 PM • 2 Y
Y by Adventure10, Mango247
No, I did not see it before.
Z K Y
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Virgil Nicula
7054 posts
Virgil Nicula
#6 h  May 19, 2016, 11:06 PM • 2 Y
Y by Adventure10, Mango247
Thank you. The your words say me that the previous inequality is own. Other interesting

inequality $:$ if $X$ , $Y$ are the projections of $E$ , $F$ on $BC\ ,$ then $XY\le \frac a2\cdot\left(\frac b{a+b}+\frac c{a+c}\right)\ .$
This post has been edited 2 times. Last edited by Virgil Nicula, Jun 26, 2016, 6:20 PM
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arqady
30161 posts
arqady
#9 h  Jun 26, 2016, 6:56 AM • 1 Y
Y by Adventure10
Are these projections to $BC$?
This post has been edited 1 time. Last edited by arqady, Jun 26, 2016, 6:56 AM
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Virgil Nicula
7054 posts
Virgil Nicula
#10 h  Jun 26, 2016, 6:24 PM • 1 Y
Y by Adventure10
Sorry! Yes, I edited now.
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