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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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Inequalities
sqing   2
N 3 minutes ago by sqing
Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=11.$ Prove that
$$a+ab+abc\leq\frac{49}{6}$$Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=10.$ Prove that
$$a+ab+abc\leq\frac{169}{24}$$Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=14.$ Prove that
$$a+ab+abc\leq\frac{63+5\sqrt 5}{6}$$Let $ a, b,c\geq 0 $ and $ 2a+3b+ 4c=32.$ Prove that
$$a+ab+abc\leq48+\frac{64\sqrt{2}}{3}$$
2 replies
sqing
Yesterday at 2:59 PM
sqing
3 minutes ago
J
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geometry incentre config
Tony_stark0094   1
N 7 minutes ago by Tony_stark0094
In a triangle $\Delta ABC$ $I$ is the incentre and point $F$ is defined such that $F \in AC$ and $F \in \odot BIC$
prove that $AI$ is the perpendicular bisector of $BF$
1 reply
Tony_stark0094
Yesterday at 4:09 PM
Tony_stark0094
7 minutes ago
J
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geometry
Tony_stark0094   1
N 8 minutes ago by Tony_stark0094
Consider $\Delta ABC$ let $\omega_1$ and $\omega_2$ be the circles passing through $A,B$ and $A,C$ respectively such that $BC$ is tangent to $\omega_1$ and $\omega_2$ define $R$ to be a point such that it lies on both the circles $\omega_1$ and $\omega_2$ prove that $HR$ and $AR$ are perpendicular.
1 reply
Tony_stark0094
40 minutes ago
Tony_stark0094
8 minutes ago
J
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one very nice!
MihaiT   1
N 2 hours ago by MihaiT
Given $m_1$ weights, each weighing $k_1$ and another $m_2$ weights with $k_2$ each. Write a algorithm that determines the ways in which a scale can be balanced with a weight $X$ on the left pan, and display the number of possible solutions. (The weights can be placed on both pans and the program starts with the numbers $m_1,k_1,m_2,k_2,X$. What will be displayed after three successive runs: 5,2,5,1,4 | 5,2,5,1,11 | 5,2,5,1,20?

One answer is possible:
a)10;5;0;
b)20;7;0;
c)20;7;1;
d)10;10;0;
e)10;7;0;
f)20;5;0,
1 reply
MihaiT
Mar 31, 2025
MihaiT
2 hours ago
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No more topics!
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J
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Geometry problem
greenapple2   3
N Jan 29, 2020 by jayme
Let K be the circle passing through all four corners of a square ABCD. Let P be a point on the minor arc CD, different from C and D. The line AP meets the line BD at X and the line CP meets the line BD at Y. Let M be the midpoint of XY.

Prove that MP is tangent to K.
3 replies
greenapple2
Dec 4, 2019
jayme
Jan 29, 2020
J
Geometry problem
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Reveal topic tags
geometry
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greenapple2
5 posts
greenapple2
#1 h  Dec 4, 2019, 2:10 PM • 2 Y
Y by Adventure10, Mango247
Let K be the circle passing through all four corners of a square ABCD. Let P be a point on the minor arc CD, different from C and D. The line AP meets the line BD at X and the line CP meets the line BD at Y. Let M be the midpoint of XY.

Prove that MP is tangent to K.
Z K Y
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Leo142857
128 posts
Leo142857
#4 h  Dec 4, 2019, 2:39 PM • 2 Y
Y by Adventure10, Mango247
We denote the center of circle as O

As AC is also a diameter of the circle K,
we’ll note that < YPX is a right angle,

Now we shall write < MXP and < MPX as sums of arcs
<MXP = (1/2)(arcAD + arcDP) = 1/2(arcAP)
whereas,
<MPX = (1/2)(arcAD + arcDP) = 1/2(arcAP)

Meaning that both <MXP= < MPX
Which leads to MP=MX
As triangleXPY is a right triangle, we conclude that M is the midpoint of XY.
Now we need to still proof that <OPM is a right angle,
Which is evident as <MPD = <DBP = <XPB
We are done.
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jayme
9774 posts
jayme
#5 h  Dec 5, 2019, 8:42 AM • 1 Y
Y by Adventure10
Dear Mathlinkers,

1. L the circumcircle of the triangle PXT
2. L and K are orthogonal and we are done...

Sincerely
Jean-Louis
Z K Y
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jayme
9774 posts
jayme
#6 h  Jan 29, 2020, 12:39 PM • 1 Y
Y by Adventure10
Dear Mathlinkers,

http://jl.ayme.pagesperso-orange.fr/Docs/Miniatures%20Geometriques%20addendum%20VI.pdf p. 76...

Sincerely
Jean-Louis
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