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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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Reflections of AB, AC with respect to BC and angle bisector of A
falantrng   26
N 4 minutes ago by ehuseyinyigit
Source: BMO 2024 Problem 1
Let $ABC$ be an acute-angled triangle with $AC > AB$ and let $D$ be the foot of the
$A$-angle bisector on $BC$. The reflections of lines $AB$ and $AC$ in line $BC$ meet $AC$ and $AB$ at points
$E$ and $F$ respectively. A line through $D$ meets $AC$ and $AB$ at $G$ and $H$ respectively such that $G$
lies strictly between $A$ and $C$ while $H$ lies strictly between $B$ and $F$. Prove that the circumcircles of
$\triangle EDG$ and $\triangle FDH$ are tangent to each other.
26 replies
falantrng
Apr 29, 2024
ehuseyinyigit
4 minutes ago
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configurational geometry as usual
GorgonMathDota   11
N 11 minutes ago by ratavir
Source: Indonesia National Math Olympiad 2021 Problem 7 (INAMO 2021/7)
Given $\triangle ABC$ with circumcircle $\ell$. Point $M$ in $\triangle ABC$ such that $AM$ is the angle bisector of $\angle BAC$. Circle with center $M$ and radius $MB$ intersects $\ell$ and $BC$ at $D$ and $E$ respectively, $(B \not= D, B \not= E)$. Let $P$ be the midpoint of arc $BC$ in $\ell$ that didn't have $A$. Prove that $AP$ angle bisector of $\angle DPE$ if and only if $\angle B = 90^{\circ}$.
11 replies
GorgonMathDota
Nov 9, 2021
ratavir
11 minutes ago
J
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kind of well known?
dotscom26   1
N 44 minutes ago by dotscom26
Source: MBL
Let $ y_1, y_2, ..., y_{2025}$ be real numbers satisfying
$ y_1^2 + y_2^2 + \cdots + y_{2025}^2 = 1. $
Find the maximum value of
$ |y_1 - y_2| + |y_2 - y_3| + \cdots + |y_{2025} - y_1|. $

I have seen many problems with the same structure, Id really appreciate if someone could explain which approach is suitable here
1 reply
+1 w
dotscom26
Today at 4:11 AM
dotscom26
44 minutes ago
J
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sum(ab/4a^2+b^2) <= 3/5
truongphatt2668   2
N an hour ago by arqady
Source: I remember I read it somewhere
Let $a,b,c>0$. Prove that:
$$\dfrac{ab}{a^2+4b^2} + \dfrac{bc}{b^2+4c^2} + \dfrac{ca}{c^2+4a^2} \le \dfrac{3}{5}$$
2 replies
1 viewing
truongphatt2668
Yesterday at 1:23 PM
arqady
an hour ago
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No more topics!
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orthocenter of MNK is the circumcenter of the inscribed hexagon
parmenides51   1
N Jun 28, 2020 by WolfusA
Source: 1996 Argentina OMA L3 p3
The non-regular hexagon $ABCDEF$ is inscribed on a circle of center $O$ and $AB = CD = EF$. If diagonals $AC$ and $BD$ intersect at $M$, diagonals $CE$ and $DF$ intersect at $N$, and diagonals $AE$ and $BF$ intersect at $K$, show that the heights of triangle $MNK$ intersect at $O$.
1 reply
parmenides51
Jun 11, 2020
WolfusA
Jun 28, 2020
J
orthocenter of MNK is the circumcenter of the inscribed hexagon
G H J
Reveal topic tags
geometry
circumcircle
hexagon
Circumcenter
orthocenter
L
G H BBookmark kLocked kLocked NReply
Source: 1996 Argentina OMA L3 p3
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parmenides51
30629 posts
parmenides51
#1 h  Jun 11, 2020, 4:22 AM
Y by
The non-regular hexagon $ABCDEF$ is inscribed on a circle of center $O$ and $AB = CD = EF$. If diagonals $AC$ and $BD$ intersect at $M$, diagonals $CE$ and $DF$ intersect at $N$, and diagonals $AE$ and $BF$ intersect at $K$, show that the heights of triangle $MNK$ intersect at $O$.
This post has been edited 1 time. Last edited by parmenides51, Jun 11, 2020, 4:53 AM
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WolfusA
1900 posts
WolfusA
#2 h  Jun 28, 2020, 1:38 PM • 2 Y
Y by Mango247, ehuseyinyigit
Via symmetry in variables it's sufficient to prove $KO\perp MN$. We have$$AB=EF\implies \measuredangle MCN=\measuredangle ACE=\measuredangle BDF=\measuredangle MDN$$thus points $M,C,D,N$ are concyclic. Hence $$\measuredangle CMN=\measuredangle CDN=\measuredangle CDF=\measuredangle CAF\implies MN\parallel AF$$Quadrilateral $ABEF$ is an isosceles trapezoid so$$KO\perp AF\parallel MN$$
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