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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

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[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
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How inflated are current aime/amc problems
derekli   2
N 16 minutes ago by Mathgloggers
So I've been working on a math grinding tool in Stellar Learning (https://stellarlearning.app/competitive) and I was wondering how to make an algorithm that can calculate the difficulty of a problem. Specifically I want to know how difficult past AIMEs and AMC 10s and other contests are, compared to our current contests. I'm planning to make a problem ELO system similar to mathdash or something like that. Any help would be appreciated! Again if you would like to support me you may consider joining our developer team! :D
2 replies
derekli
5 hours ago
Mathgloggers
16 minutes ago
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2023 Official Mock NAIME #15 f(f(f(x))) = f(f(x))
parmenides51   1
N 2 hours ago by jasperE3
How many non-bijective functions $f$ exist that satisfy $f(f(f(x))) = f(f(x))$ for all real $x$ and the domain of f is strictly within the set of $\{1,2,3,5,6,7,9\}$, the range being $\{1,2,4,6,7,8,9\}$?

Even though this is an AIME problem, a proof is mandatory for full credit. Constants must be ignored as we dont want an infinite number of solutions.
1 reply
parmenides51
Dec 4, 2023
jasperE3
2 hours ago
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Inequalities
sqing   3
N 3 hours ago by sqing
Let $ a,b>0 $ and $\frac{a}{a^2+3}+ \frac{b}{b^2+ 3} \geq \frac{1}{2} . $ Prove that
$$a^2+ab+b^2\geq 3$$$$a^2-ab+b^2 \geq 1 $$Let $ a,b>0 $ and $\frac{a}{a^3+3}+ \frac{b}{b^3+ 3}\geq \frac{1}{2} . $ Prove that
$$a^3+ab+b^3 \geq 3$$$$ a^3-ab+b^3\geq 1 $$
3 replies
sqing
Wednesday at 12:59 PM
sqing
3 hours ago
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exist solutions?
teomihai   6
N Today at 12:05 AM by iwastedmyusername
Find how many perfect squares of five different digits there are, with elements from the set ${0,1,4,6,9}$.
6 replies
teomihai
Yesterday at 5:04 PM
iwastedmyusername
Today at 12:05 AM
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Geometry Basic
AlexCenteno2007   4
N May 4, 2025 by giratina3
Let $ABC$ be an isosceles triangle such that $AC=BC$. Let $P$ be a dot on the $AC$ side.
The tangent to the circumcircle of $ABP$ at point $P$ intersects the circumcircle of $BCP$ at $D$. Prove that CD$ \parallel$AB
4 replies
AlexCenteno2007
Apr 28, 2025
giratina3
May 4, 2025
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Geometry Basic
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Reveal topic tags
geometry
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AlexCenteno2007
150 posts
AlexCenteno2007
#1 h  Apr 28, 2025, 12:11 AM
Y by
Let $ABC$ be an isosceles triangle such that $AC=BC$. Let $P$ be a dot on the $AC$ side.
The tangent to the circumcircle of $ABP$ at point $P$ intersects the circumcircle of $BCP$ at $D$. Prove that CD$ \parallel$AB
This post has been edited 5 times. Last edited by AlexCenteno2007, Apr 28, 2025, 12:14 AM
Reason: Error
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AlexCenteno2007
150 posts
AlexCenteno2007
#3 h  Apr 28, 2025, 1:44 AM
Y by
Could you give any clues?
This post has been edited 1 time. Last edited by AlexCenteno2007, Apr 28, 2025, 4:16 PM
Reason: Error
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mathafou
420 posts
mathafou
#4 h  Apr 28, 2025, 5:58 PM • 1 Y
Y by AlexCenteno2007
hint
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AlexCenteno2007
150 posts
AlexCenteno2007
#5 h  May 4, 2025, 3:00 AM
Y by
mathafou wrote:
hint

I guess that by power of points it can come out, right?
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giratina3
526 posts
giratina3
#6 h  May 4, 2025, 3:18 AM
Y by
Chasing inscribed angles would definitely be the first step to solving the problem.
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