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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
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
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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Number Theory with set and subset and divisibility
SomeonecoolLovesMaths   3
N 39 minutes ago by martianrunner
Let $S = \{ 1,2, \cdots, 100 \}$. Let $A$ be a subset of $S$ such that no sum of three distinct elements of $A$ is divisible by $5$. What is the maximum value of $\mid A \mid$.
3 replies
SomeonecoolLovesMaths
Apr 21, 2025
martianrunner
39 minutes ago
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Basic geometry
AlexCenteno2007   7
N 40 minutes ago by KAME06
Given an isosceles triangle ABC with AB=BC, the inner bisector of Angle BAC And cut next to it BC in D. A point E is such that AE=DC. The inner bisector of the AED angle cuts to the AB side at the point F. Prove that the angle AFE= angle DFE
7 replies
AlexCenteno2007
Feb 9, 2025
KAME06
40 minutes ago
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Generating Functions
greenplanet2050   7
N 44 minutes ago by rchokler
So im learning generating functions and i dont really understand why $1+2x+3x^2+4x^3+5x^4+…=\dfrac{1}{(1-x)^2}$

can someone help

thank you :)
7 replies
greenplanet2050
Yesterday at 10:42 PM
rchokler
44 minutes ago
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Algebraic Manipulation
Darealzolt   1
N 3 hours ago by Soupboy0
Find the number of pairs of real numbers $a, b, c$ that satisfy the equation $a^4 + b^4 + c^4 + 1 = 4abc$.
1 reply
1 viewing
Darealzolt
4 hours ago
Soupboy0
3 hours ago
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equilateral inside a circle, with base parallel to diameter (Chile 2008 L1 P2)
parmenides51   1
N May 27, 2019 by brainiacmaniac31
In a circle of radius $1$ a diameter $PQ$ is drawn and an equilateral triangle with base $AB$ parallel to $PQ$ is inscribed. The segment $PQ$ cuts to the side $BC$ at the point $R$. Is the length $PR$ smaller, equal, or greater than the length of a quarter of the circumference?
IMAGE
1 reply
parmenides51
May 26, 2019
brainiacmaniac31
May 27, 2019
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equilateral inside a circle, with base parallel to diameter (Chile 2008 L1 P2)
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Reveal topic tags
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circle
Equilateral Triangle
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parmenides51
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parmenides51
#1 h  May 26, 2019, 7:36 PM • 2 Y
Y by Adventure10, Mango247
In a circle of radius $1$ a diameter $PQ$ is drawn and an equilateral triangle with base $AB$ parallel to $PQ$ is inscribed. The segment $PQ$ cuts to the side $BC$ at the point $R$. Is the length $PR$ smaller, equal, or greater than the length of a quarter of the circumference?
https://cdn.artofproblemsolving.com/attachments/a/d/f11bdbd06f011fc6cf474fc566d941b9370950.png
This post has been edited 1 time. Last edited by parmenides51, Oct 19, 2021, 9:22 PM
Reason: added image
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brainiacmaniac31
2170 posts
brainiacmaniac31
#2 h  May 27, 2019, 12:00 AM • 4 Y
Y by Adventure10, Mango247, Mango247, Mango247
Since $\frac{\sqrt{3}}{3}+1\ge \frac{\pi}{2}$, the length $PR$ is greater.
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