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k a April Highlights and 2025 AoPS Online Class Information
jlacosta   0
Apr 2, 2025
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
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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0 replies
jlacosta
Apr 2, 2025
0 replies
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1 line solution to Inequality
ItzsleepyXD   2
N 2 minutes ago by Vivaandax
Source: Own , Mock Thailand Mathematic Olympiad P8
Let $x_1,x_2,\dots,x_n$ be positive real integer such that $x_1^2+x_2^2+\cdots+x_n^2=2$ Prove that
$$\sum_{i=1}^{n}\frac{1}{x_i^3(x_{i-1}+x_{i+1})}\geqslant \left(\sum_{i=1}^{n}\frac{x_i}{x_{i-1}+x_{i+1}}\right)^3$$such that $x_{n+1}=x_1$ and $x_0=x_n$
2 replies
ItzsleepyXD
Today at 9:27 AM
Vivaandax
2 minutes ago
J
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Cool functional equation
Rayanelba   1
N 6 minutes ago by NO_SQUARES
Source: Own
Find all functions $f:\mathbb{Z}_{>0}\to \mathbb{Z}_{>0}$ that verify the following equation for all $x,y\in \mathbb{Z}_{>0}$:
$max(f^{f(y)}(x),f^{f(y)}(y))|min(x,y)$
1 reply
Rayanelba
14 minutes ago
NO_SQUARES
6 minutes ago
J
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primes,exponentials,factorials
skellyrah   2
N 35 minutes ago by CM1910
find all primes p,q such that $$ \frac{p^q+q^p-p-q}{p!-q!} $$is a prime number
2 replies
skellyrah
an hour ago
CM1910
35 minutes ago
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Queue geo
vincentwant   1
N an hour ago by hukilau17
Let $ABC$ be an acute scalene triangle with circumcenter $O$. Let $Y, Z$ be the feet of the altitudes from $B, C$ to $AC, AB$ respectively. Let $D$ be the midpoint of $BC$. Let $\omega_1$ be the circle with diameter $AD$. Let $Q\neq A$ be the intersection of $(ABC)$ and $\omega$. Let $H$ be the orthocenter of $ABC$. Let $K$ be the intersection of $AQ$ and $BC$. Let $l_1,l_2$ be the lines through $Q$ tangent to $\omega,(AYZ)$ respectively. Let $I$ be the intersection of $l_1$ and $KH$. Let $P$ be the intersection of $l_2$ and $YZ$. Let $l$ be the line through $I$ parallel to $HD$ and let $O'$ be the reflection of $O$ across $l$. Prove that $O'P$ is tangent to $(KPQ)$.
1 reply
vincentwant
4 hours ago
hukilau17
an hour ago
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No more topics!
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2 lines concurrent with a circle, 3 more circles related
parmenides51   0
Oct 24, 2021
Source: 2015 Centroamerican Shortlist G7 https://artofproblemsolving.com/community/c2452548_centroamerican_shortlist__geometry
Let $ABC$ be a triangle and let $\omega_A$ and $\omega_B$ be the circles that pass through $C$ and are tangent to $AB$ at $A$ and $B$, respectively. Circles $\omega_A$ and $\omega_B$ intersect at $C$ and $N$. Let $M$ be the intersection of $CN$ with $AB$. Let $\Omega$ be the circle that passes through $C$ and is tangent to $AB$ at $M$, and let $\omega$ be the circle tangent to $\Omega$ passing through $C$ and $N$. The tangents to $\omega$ from $M$ intersect $\omega$ at $X$ and $Y$. Let $Z$ be the intersection point of $AX$ and $BY$. Prove that $Z$ lies on $\omega$.
0 replies
parmenides51
Oct 24, 2021
0 replies
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2 lines concurrent with a circle, 3 more circles related
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Reveal topic tags
concurrency
concurrent
circles
geometry
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Source: 2015 Centroamerican Shortlist G7 https://artofproblemsolving.com/community/c2452548_centroamerican_shortlist__geometry
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parmenides51
30650 posts
parmenides51
#1 h  Oct 24, 2021, 9:50 PM
Y by
Let $ABC$ be a triangle and let $\omega_A$ and $\omega_B$ be the circles that pass through $C$ and are tangent to $AB$ at $A$ and $B$, respectively. Circles $\omega_A$ and $\omega_B$ intersect at $C$ and $N$. Let $M$ be the intersection of $CN$ with $AB$. Let $\Omega$ be the circle that passes through $C$ and is tangent to $AB$ at $M$, and let $\omega$ be the circle tangent to $\Omega$ passing through $C$ and $N$. The tangents to $\omega$ from $M$ intersect $\omega$ at $X$ and $Y$. Let $Z$ be the intersection point of $AX$ and $BY$. Prove that $Z$ lies on $\omega$.
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