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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
J
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Angles, similar triangles, geometry problem
smalkaram_3549   0
4 minutes ago
Completely stuck on this problem.
0 replies
smalkaram_3549
4 minutes ago
0 replies
J
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Conditional maximum
giangtruong13   2
N 7 minutes ago by sqing
Source: Specialized Math
Let $a,b$ satisfy that: $1 \leq a \leq2$ and $1 \leq b \leq 2$. Find the maximum: $$A=(a+b^2+\frac{4}{a^2}+\frac{2}{b})(b+a^2+\frac{4}{b^2}+\frac{2}{a})$$
2 replies
1 viewing
giangtruong13
Mar 22, 2025
sqing
7 minutes ago
J
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inequality ( 4 var
SunnyEvan   3
N 20 minutes ago by SunnyEvan
Let $ a,b,c,d \in R $ , such that $ a+b+c+d=4 . $ Prove that :
$$ a^4+b^4+c^4+d^4+3 \geq \frac{7}{4}(a^3+b^3+c^3+d^3) $$$$ a^4+b^4+c^4+d^4+ \frac{252}{25} \geq \frac{88}{25}(a^3+b^3+c^3+d^3) $$equality cases : ?
3 replies
SunnyEvan
Yesterday at 5:19 AM
SunnyEvan
20 minutes ago
J
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Inspired by JK1603JK
sqing   16
N 24 minutes ago by sqing
Source: Own
Let $ a,b,c\geq 0 $ and $ab+bc+ca=1.$ Prove that$$\frac{abc-2}{abc-1}\ge \frac{4(a^2b+b^2c+c^2a)}{a^3b+b^3c+c^3a+1} $$
16 replies
sqing
Yesterday at 3:31 AM
sqing
24 minutes ago
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rotation triangle
sahadian   2
N Feb 22, 2013 by sunken rock
Let $ABC$ be a triangle with $AB\neq AC$, and let $A_{1}B_{1}C_{1}$ be the image of triangle $ABC$ through a rotation $R$ centered at $C$.
Let $M,E , F$ be the midpoints of the segments $BA_{1}, AC, BC_{1}$ respectively
Given that $EM = FM$, compute $\angle EMF$.
2 replies
sahadian
Feb 18, 2013
sunken rock
Feb 22, 2013
J
rotation triangle
G H J
Reveal topic tags
geometry
geometric transformation
rotation
geometry unsolved
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sahadian
112 posts
sahadian
#1 h  Feb 18, 2013, 7:59 PM • 2 Y
Y by Adventure10, Rounak_iitr
Let $ABC$ be a triangle with $AB\neq AC$, and let $A_{1}B_{1}C_{1}$ be the image of triangle $ABC$ through a rotation $R$ centered at $C$.
Let $M,E , F$ be the midpoints of the segments $BA_{1}, AC, BC_{1}$ respectively
Given that $EM = FM$, compute $\angle EMF$.
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sahadian
112 posts
sahadian
#2 h  Feb 20, 2013, 6:38 PM • 2 Y
Y by Adventure10, Mango247
I only find that $\angle AMC=90$
someone help me to solve this question
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sunken rock
4379 posts
sunken rock
#3 h  Feb 22, 2013, 5:40 PM • 2 Y
Y by Adventure10, Mango247
It seems we must have $C\equiv C'$, since the rotation is centered at $C$.

Best regards,
sunken rock
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