It's February and we'd love to help you find the right course plan!

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k a February Highlights and 2025 AoPS Online Class Information
jlacosta   0
Feb 2, 2025
We love to share what you can look forward to this month! The AIME I and AIME II competitions are happening on February 6th and 12th, respectively. Join our Math Jams the day after each competition where we will go over all the problems and the useful strategies to solve them!

2025 AIME I Math Jam: Difficulty Level: 8* (Advanced math)
February 7th (Friday), 4:30pm PT/7:30 pm ET

2025 AIME II Math Jam: Difficulty Level: 8* (Advanced math)
February 13th (Thursday), 4:30pm PT/7:30 pm ET

The F=ma exam will be held on February 12th. Check out our F=ma Problem Series course that begins February 19th if you are interested in participating next year! The course will prepare you to take the F=ma exam, the first test in a series of contests that determines the members of the US team for the International Physics Olympiad. You'll learn the classical mechanics needed for the F=ma exam as well as how to solve problems taken from past exams, strategies to succeed, and you’ll take a practice F=ma test of brand-new problems.

Mark your calendars for all our upcoming events:
[list][*]Feb 7, 4:30 pm PT/7:30pm ET, 2025 AIME I Math Jam
[*]Feb 12, 4pm PT/7pm ET, Mastering Language Arts Through Problem-Solving: The AoPS Method
[*]Feb 13, 4:30 pm PT/7:30pm ET, 2025 AIME II Math Jam
[*]Feb 20, 4pm PT/7pm ET, The Virtual Campus Spring Experience[/list]
AoPS Spring classes are open for enrollment. Get a jump on 2025 and enroll in our math, contest prep, coding, and science classes today! Need help finding the right plan for your goals? Check out our recommendations page!

Don’t forget: Highlight your AoPS Education on LinkedIn!
Many of you are beginning to build your education and achievements history on LinkedIn. Now, you can showcase your courses from Art of Problem Solving (AoPS) directly on your LinkedIn profile! Don't miss this opportunity to stand out and connect with fellow problem-solvers in the professional world and be sure to follow us at: https://www.linkedin.com/school/art-of-problem-solving/mycompany/ Check out our job postings, too, if you are interested in either full-time, part-time, or internship opportunities!

Our full course list for upcoming classes is below:
All classes run 7:30pm-8:45pm ET/4:30pm - 5:45pm PT unless otherwise noted.

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Sat & Sun, Feb 1 - Feb 2 (4:00 - 7:00 pm ET/1:00 - 4:00 pm PT)

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Wednesday, Feb 19 - May 7

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0 replies
jlacosta
Feb 2, 2025
0 replies
Combinatorics
a-mathematician-student   1
N an hour ago by hunterlyh
22 trees are arranged in a circle; on each tree, there is a crow.
Every minute, two crows each move to a neighboring tree.
Is it possible for all the crows, after a certain number of minutes, to gather on the same tree?
1 reply
1 viewing
a-mathematician-student
5 hours ago
hunterlyh
an hour ago
[PMO26 Qualifying III.7] Max Distinct Integers
kae_3   2
N 2 hours ago by jasperE3
For positive integers $i,j,k,l$ less than $5$, let $A_{ijkl}$ be an integer. Suppose that the integers $A_{ijkl}$ satisfy the following properties.

(a) $A_{ijkl}=-A_{jikl}$;
(b) $A_{ijkl}=-A_{ijlk}$;
(c) $A_{ijkl}=+A_{klij}$.

What is the maximum number of distinct integers $A_{ijkl}$?

Answer Confirmation
2 replies
kae_3
Sunday at 8:40 PM
jasperE3
2 hours ago
Prove S=Q+
toanrathay   13
N 2 hours ago by jasperE3
Let $S$ be a set of rational numbers satisfying
$\bullet$ $S$ contains at least one positive element
$\bullet$ $0\not\in S$
$\bullet$ If $a,b\in S$, then $a+b\in S$
$\bullet$ For all rational number $a\neq 0$, either $a$ or $-a$ is in $S$
Prove that $S$ contains all positive rational number.
13 replies
toanrathay
Yesterday at 3:57 PM
jasperE3
2 hours ago
polynomial
hoangvu1009   1
N 3 hours ago by mathafou
A polynomial $P(x)$ has degree at most 4, with its highest coefficient being 2. Given that:
\[ P(1) = 1, P(2) = 4, P(3) = 9, P(4) = 15, \]find $P(5)$.
1 reply
hoangvu1009
Sunday at 6:47 PM
mathafou
3 hours ago
No more topics!
Chord in a circle
chess64   3
N Jun 24, 2006 by mathgeniuse^ln(x)
$DEB$ is a chord of a circle such that $DE=3$ and $EB=5$. Let $O$ be the centre of the circle. Join $OE$ and extend $OE$ to cut the circle at $C$. (See diagram). Given $EC=1$, find the radius of the circle.

IMAGE
3 replies
chess64
Jun 24, 2006
mathgeniuse^ln(x)
Jun 24, 2006
Chord in a circle
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chess64
4794 posts
#1 • 2 Y
Y by Adventure10, Mango247
$DEB$ is a chord of a circle such that $DE=3$ and $EB=5$. Let $O$ be the centre of the circle. Join $OE$ and extend $OE$ to cut the circle at $C$. (See diagram). Given $EC=1$, find the radius of the circle.

[asy]
size(6cm);

pair O = (0,0), B = dir(110), D = dir(30), E = 0.4 * B + 0.6 * D, C = intersectionpoint(O--2*E, unitcircle);

draw(unitcircle);
draw(O--C);
draw(B--D);

dot(O);
dot(B);
dot(C);
dot(D);
dot(E);

label("$B$", B, B);
label("$C$", C, C);
label("$D$", D, D);
label("$E$", E, dir(280));
label("$O$", O, dir(270));
[/asy]
This post has been edited 2 times. Last edited by djmathman, Aug 24, 2016, 3:57 PM
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ch1n353ch3s54a1l
1461 posts
#2 • 2 Y
Y by Adventure10, Mango247
chess64 wrote:
$DEB$ is a chord of a circle such that $DE=3$ and $EB=5$. Let $O$ be the centre of the circle. Join $OE$ and extend $OE$ to cut the circle at $C$. (See diagram). Given $EC=1$, find the radius of the circle.

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sapphyre571
357 posts
#3 • 2 Y
Y by Adventure10, Mango247
that is correct
the chord-chord power theorem states that in a circle with noncollinear chords AB and CD intersecting at E
then (AE)(EB)=(CE)(ED)
or 3*5=1*2x-1 (I use 2x-1 instead of 2x+1 because it elimiates adding 1 - yes I am that lazy (or efficient if you want to be nice about it))
in this case, one of the chords is the diameter so solving for the length of that diameter, (CE+OE+OF where F is the point on circle O diametrically opposite C)
this solves for x, the length of the radius
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mathgeniuse^ln(x)
5020 posts
#4 • 1 Y
Y by Adventure10
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