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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)!

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[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 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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Eazy equation clap
giangtruong13   0
an hour ago
Find all $x,y,z$ satisfy that: $$\frac{x}{y+z}=2x-1; \frac{y}{x+z}=3y-1;\frac{z}{x+y}=5x-1$$
0 replies
giangtruong13
an hour ago
0 replies
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inequality
revol_ufiaw   3
N 2 hours ago by MS_asdfgzxcvb
Prove that that for any real $x \ge 0$ and natural number $n$,
$$x^n (n+1)^{n+1} \le n^n (x+1)^{n+1}.$$
3 replies
revol_ufiaw
3 hours ago
MS_asdfgzxcvb
2 hours ago
J
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How to judge a number is prime or not?
mingzhehu   0
3 hours ago
A=（10X1+1）(10X+1），X1，X∈N+
B=（10 X1+3）（10X+7），X∈N，X1∈N
C=(10 X1+9)(10X+9), X∈N，X1∈N
D=(10 X1+1)(10X+3), X1∈N+，X∈N
E=（10 X1+7）(10X+9），X∈N，X1∈N
F=（10 X1+1）（10X+7），X1∈N+，X∈N
G=（10 X1+3）（10X+9），X∈N，X1∈N
H=（10 X1+1）10X+9），X1∈N+，X∈N
I=（10 X1+3）（10X+3），X1∈N，X∈N
J=( 10X1+7)(10X+7),X∈N，X1∈N

For any natural number P∈{P=10N+1，n∈N}，make P=A or B or C
If P can make the roots of function group(ABC) without any root group completely made up of integer, P will be a prime
For any natural number P∈{P=10N+3，n∈N}，make P=D or E
If P can make the roots of function group(DE) without any root group completely made up
of integer, P will be a prime
For any natural number P∈{P=10N+7，n∈N}，make P=F or G
If P can make the roots of function group(FG) without any root group completely made up
of integer, P will be a prime
For any natural number P∈{P=10N+9，n∈N}，make P=H or I or J
If P can make the roots of function group(GIJ) without any root group completely made up
of integer, P will be a prime
0 replies
mingzhehu
3 hours ago
0 replies
J
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What is an isogonal conjugate and why is it useful?
EaZ_Shadow   6
N 3 hours ago by maxamc
What is an isogonal conjugate and why is it useful? People use them in Olympiad geometry proofs but I don’t understand why and what is the purpose, as it complicates me because of me not understanding it.
6 replies
EaZ_Shadow
Dec 28, 2024
maxamc
3 hours ago
J
No more topics!
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computational with a tangential trapezoid (2003 Argentina OMA L2 p2)
parmenides51   1
N Jun 11, 2020 by Urvs
Given a circle of center $O$, four lines are drawn tangent to the circle so that these four lines determine the trapezoid $ABCD$, with bases $AB$ and $CD$, and non-parallel sides $BC$ and $DA$. If $AO = 2\sqrt6 , BO = 4\sqrt3$ and $CO = 4$, calculate the measures of the sides and angles of the trapezoid.
1 reply
parmenides51
Jun 11, 2020
Urvs
Jun 11, 2020
J
computational with a tangential trapezoid (2003 Argentina OMA L2 p2)
G H J
Reveal topic tags
geometry
trapezoid
tangential
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parmenides51
30629 posts
parmenides51
#1 h  Jun 11, 2020, 7:11 PM
Y by
Given a circle of center $O$, four lines are drawn tangent to the circle so that these four lines determine the trapezoid $ABCD$, with bases $AB$ and $CD$, and non-parallel sides $BC$ and $DA$. If $AO = 2\sqrt6 , BO = 4\sqrt3$ and $CO = 4$, calculate the measures of the sides and angles of the trapezoid.
Z K Y
The post below has been deleted. Click to close.
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Urvs
608 posts
Urvs
#2 h  Jun 11, 2020, 7:34 PM
Y by
In triangle ABC
<CAB+<B+<BCA= 180;
arcsin(r/AO) +2arcsin(r/BO) +arcsin(r/OC) = 180
Where r is the radius.
This post has been edited 1 time. Last edited by Urvs, Jun 11, 2020, 7:36 PM
Reason: Typos
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