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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
6 minutes ago
Spring is in full swing and summer is right around the corner, what are your plans? At AoPS Online our schedule has new classes starting now through July, so be sure to keep your skills sharp and be prepared for the Fall school year! Check out the schedule of upcoming classes below.

WOOT early bird pricing is in effect, don’t miss out! If you took MathWOOT Level 2 last year, no worries, it is all new problems this year! Our Worldwide Online Olympiad Training program is for high school level competitors. AoPS designed these courses to help our top students get the deep focus they need to succeed in their specific competition goals. Check out the details at this link for all our WOOT programs in math, computer science, chemistry, and physics.

Looking for summer camps in math and language arts? Be sure to check out the video-based summer camps offered at the Virtual Campus that are 2- to 4-weeks in duration. There are middle and high school competition math camps as well as Math Beasts camps that review key topics coupled with fun explorations covering areas such as graph theory (Math Beasts Camp 6), cryptography (Math Beasts Camp 7-8), and topology (Math Beasts Camp 8-9)!

Be sure to mark your calendars for the following events:
[list][*]April 3rd (Webinar), 4pm PT/7:00pm ET, Learning with AoPS: Perspectives from a Parent, Math Camp Instructor, and University Professor
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April 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
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[*]April 16th (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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H
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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Geo Mock #5
Bluesoul   1
N 17 minutes ago by Sedro
Consider triangle $ABC$ with $AB=13, BC=14, AC=15$. Denote the orthocenter of $\triangle{ABC}$ as $H$, the intersection of $(BHC)$ and $AC$ as $P\neq C$. Compute the length of $AP$.
1 reply
Bluesoul
Yesterday at 7:03 AM
Sedro
17 minutes ago
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Any nice way to do this?
NamelyOrange   1
N 2 hours ago by HockeyMaster85
Source: Taichung P.S.1 math program tryouts

How many ordered pairs $(a,b,c)\in\mathbb{N}^3$ are there such that $c=ab$ and $1\le a\le b\le c\le60$?
1 reply
NamelyOrange
2 hours ago
HockeyMaster85
2 hours ago
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Polynomial optimization problem
ReticulatedPython   2
N 3 hours ago by Mathzeus1024
Let $$p(x)=-ax^4+x^3$$, where $a$ is a real number. Prove that for all positive $a$, $$p(x) \le \frac{27}{256a^3}.$$
2 replies
ReticulatedPython
Mar 31, 2025
Mathzeus1024
3 hours ago
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a+b+c=3 inequality
JK1603JK   1
N 3 hours ago by KhuongTrang
Let $a,b,c\ge 0: a+b+c=3$ then prove
$$\color{black}{\sqrt{a+b+2c^{2}}+\sqrt{b+c+2a^{2}}+\sqrt{c+a+2b^{2}}\le 3\sqrt{\frac{a^2+b^2+c^2}{ab+bc+ca}+3}.}$$
1 reply
JK1603JK
4 hours ago
KhuongTrang
3 hours ago
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No more topics!
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equal segments given and wanted, midpoints (2006 Zhautykov City VII P5)
parmenides51   3
N Aug 30, 2019 by parmenides51
Let $ AF $ be the median of the triangle $ ABC $. $ D $ is the midpoint of the segment $ AF $, $ E $ is the intersection point of the line $ CD $ with the side $ AB $. It turned out that $ BD = BF = CF $. Prove that $ AE = DE $
3 replies
parmenides51
Aug 30, 2019
parmenides51
Aug 30, 2019
J
equal segments given and wanted, midpoints (2006 Zhautykov City VII P5)
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Reveal topic tags
geometry
midpoint
equal segments
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parmenides51
30629 posts
parmenides51
#1 h  Aug 30, 2019, 10:00 AM • 2 Y
Y by Adventure10, Mango247
Let $ AF $ be the median of the triangle $ ABC $. $ D $ is the midpoint of the segment $ AF $, $ E $ is the intersection point of the line $ CD $ with the side $ AB $. It turned out that $ BD = BF = CF $. Prove that $ AE = DE $
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The_Maitreyo1
1039 posts
The_Maitreyo1
#9 h  Aug 30, 2019, 6:47 PM • 1 Y
Y by Adventure10
Quite easy by COORDINATE BASHING.
Assume F to be the point $(0,0)$, B to be $(-c,0)$, C to be $(c,0)$ and A to be $(-a,b)$. Applying equality conditions on $ BD $ and $ BF $ yields: $\boxed{a^2+b^2=4ac}$
After finding the equations of $ AB $ and $ CD $, we get the coordinates of $E$. They are $\frac{-2a-c}{3}$ and $\frac{2b}{3}$. Now we just consider the side lengths of $ AE $ and $ DE $ and get the common expression as $\frac{c^2+2ac}{9}$. Done!
This post has been edited 1 time. Last edited by The_Maitreyo1, Aug 30, 2019, 6:48 PM
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amar_04
1915 posts
amar_04
#12 h  Aug 30, 2019, 7:37 PM • 2 Y
Y by Adventure10, Mango247
@above Why did you coordinate bash, it was quite simple?

Synthetic Solution
This post has been edited 5 times. Last edited by amar_04, Aug 30, 2019, 7:41 PM
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parmenides51
30629 posts
parmenides51
#13 h  Aug 30, 2019, 9:35 PM • 2 Y
Y by Adventure10, Mango247
hint
after the hint
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