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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.

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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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Inequalities
sqing   7
N an hour ago by DAVROS
Let $ a,b $ be reals such that $ a^2+ab+b^2 =3$ . Prove that
$$ \frac{4}{ 3}\geq \frac{1}{ a^2+5 }+ \frac{1}{ b^2+5 }+ab \geq -\frac{11}{4 }$$$$ \frac{13}{ 4}\geq \frac{1}{ a^2+5 }+ \frac{1}{ b^2+5 }+ab \geq -\frac{2}{3 }$$$$ \frac{3}{ 2}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }+ab \geq -\frac{17}{6 }$$$$ \frac{19}{ 6}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }-ab \geq -\frac{1}{2}$$Let $ a,b $ be reals such that $ a^2-ab+b^2 =1 $ . Prove that
$$ \frac{3}{ 2}\geq \frac{1}{ a^2+3 }+ \frac{1}{ b^2+3 }+ab \geq \frac{4}{15 }$$$$ \frac{14}{ 15}\geq \frac{1}{ a^2+3 }+ \frac{1}{ b^2+3 }-ab \geq -\frac{1}{2 }$$$$ \frac{3}{ 2}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }+ab \geq \frac{13}{42 }$$$$ \frac{41}{ 42}\geq \frac{1}{ a^4+3 }+ \frac{1}{ b^4+3 }-ab \geq -\frac{1}{2 }$$
7 replies
sqing
Apr 16, 2025
DAVROS
an hour ago
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JEE Related ig?
mikkymini2   16
N an hour ago by mikkymini2
Hey everyone,

Just wanted to see if there are any other JEE aspirants on this forum currently prepping for it[mention year if you can]

I am actually entering 10th this year and have decided to try for it...So this year is just going to go in me strengthening my math (IOQM level (heard its enough till Mains part, so will start from there) for the problem solving part, and learn some topics from 11th and 12th as well)

It would be great to connect with others who are going through the same thing - share study strategies, tips, resources, discuss, and maybe even form study groups(not sure how to tho :maybe: ) and motivate each other ig?. :D
So yea, cya later
16 replies
mikkymini2
Apr 10, 2025
mikkymini2
an hour ago
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Leibnitz theorem?
soryn   2
N 4 hours ago by soryn
If M îs a interior point of the triangle ABC, and Ga,GB,GC are the centoids of triangles MBC, MAC and MAB, respectively, G0 is the centroid of triangle GaGbGc, show that the line MG0 passes through a fixed point.
2 replies
soryn
5 hours ago
soryn
4 hours ago
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simplfy this
Miranda2829   6
N Today at 12:26 AM by Miranda2829
4b+13/ -4b+15 = 1/6

anyone can help on the steps to do this ? thank u
6 replies
Miranda2829
Apr 16, 2025
Miranda2829
Today at 12:26 AM
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No more topics!
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area wanted, right triangle, medians (2013 AMQ Concours College p1)
parmenides51   6
N Mar 14, 2021 by HamstPan38825
Jacqueline wants to calculate the area of triangle $NMI$ with right angle at $I$. She knows that the medians $MD$ and $NE$ intersect at $O$. She also knows that $OD=3$ and $OE=4$. What is the area of triangle $NMI$?
6 replies
parmenides51
Mar 14, 2021
HamstPan38825
Mar 14, 2021
J
area wanted, right triangle, medians (2013 AMQ Concours College p1)
G H J
Reveal topic tags
geometry
right triangle
area
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G H BBookmark kLocked kLocked NReply
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parmenides51
30629 posts
parmenides51
#1 h  Mar 14, 2021, 3:32 PM • 3 Y
Y by centslordm, tenebrine, samrocksnature
Jacqueline wants to calculate the area of triangle $NMI$ with right angle at $I$. She knows that the medians $MD$ and $NE$ intersect at $O$. She also knows that $OD=3$ and $OE=4$. What is the area of triangle $NMI$?
This post has been edited 2 times. Last edited by parmenides51, Mar 14, 2021, 7:57 PM
Reason: changed wording, removed ''breaking her head with the triangle part''
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MathArt4
3674 posts
MathArt4
#2 h  Mar 14, 2021, 3:42 PM • 1 Y
Y by tenebrine
Solution
This post has been edited 1 time. Last edited by MathArt4, Mar 14, 2021, 3:42 PM
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recoco
287 posts
recoco
#3 h  Mar 14, 2021, 3:46 PM • 2 Y
Y by sotpidot, tenebrine
"Jacqueline is breaking her head with a triangle"
hmmmm, thats kinda sus
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HamstPan38825
8857 posts
HamstPan38825
#4 h  Mar 14, 2021, 4:23 PM • 1 Y
Y by tenebrine
@#3
Are you sure the translation is correct :rotfl:
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parmenides51
30629 posts
parmenides51
#5 h  Mar 14, 2021, 4:32 PM • 1 Y
Y by tenebrine
original wording in French

I used google translate and when I looked for ''break my head'' in internet it gave me among others the translation ''puzzle'' , so it seemed somewhat ok
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natmath
8219 posts
natmath
#6 h  Mar 14, 2021, 4:38 PM • 1 Y
Y by tenebrine
Ik this is off topic, but this reminds me that spanish has a similar literal translation for puzzle that translates to something like head breaker.
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HamstPan38825
8857 posts
HamstPan38825
#7 h  Mar 14, 2021, 6:36 PM • 3 Y
Y by tenebrine, Mango247, Mango247
@#5
tenebrine and cents casually upvote lol

can you change the wording of the OP?
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