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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
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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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inequalities - 5/4
pennypc123456789   1
N 20 minutes ago by Mathzeus1024
Given real numbers $x, y$ satisfying $|x| \le 3, |y| \le 3$. Prove that:
\[ 0 \le (x^2 + 1)(y^2 + 1) + 4(x - 1)(y - 1) \le 164. \]
1 reply
pennypc123456789
2 hours ago
Mathzeus1024
20 minutes ago
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.problem.
Cobedangiu   3
N an hour ago by Cobedangiu
Find the integer coefficients after expanding Newton's binomial:
$$(\frac{3}{2}-\frac{2}{3}x^2)^n (n \in Z)$$
3 replies
Cobedangiu
Yesterday at 6:20 AM
Cobedangiu
an hour ago
J
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Source of a combinatorics problem
isodynamicappolonius2903   0
4 hours ago
Does anyone know exactly the source of this problem?? I just remember that it from a combinatorics book of Russia.
0 replies
isodynamicappolonius2903
4 hours ago
0 replies
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KSEA NMSC Mock Contest Group B (Last Problem)
Shiyul   5
N Today at 3:26 AM by Shiyul
Let $a_n$ be a sequence defined by $a_n = a^2 + 1$. Then the product of four consecutive terms in $a_n$ can be written as the product of two terms in $a_n$. Find $p + q$ if $(a_(11))(a_(12))(a_(13))(a_(14)) = (a_p)(a_q)$.
5 replies
Shiyul
Yesterday at 3:09 PM
Shiyul
Today at 3:26 AM
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EF//AB wanted in right triangle 2014 Armenia NMO 9.2
parmenides51   2
N Aug 17, 2021 by musan1909
Given a right triangle $ABC$ ( $\angle C = 90 ^ \circ$). The altitude $CH$ intersect angle bisectors $AK$ and $BL$ at the points $ P$ and $Q$, respectively. Let $F$ and $E$ be the midpoints of the segments $PK$ and $QL$ respectively. Prove that $EF$ is parallel to $AB$.
2 replies
parmenides51
Aug 16, 2021
musan1909
Aug 17, 2021
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EF//AB wanted in right triangle 2014 Armenia NMO 9.2
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Reveal topic tags
geometry
parallel
right triangle
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parmenides51
30629 posts
parmenides51
#1 h  Aug 16, 2021, 10:29 PM
Y by
Given a right triangle $ABC$ ( $\angle C = 90 ^ \circ$). The altitude $CH$ intersect angle bisectors $AK$ and $BL$ at the points $ P$ and $Q$, respectively. Let $F$ and $E$ be the midpoints of the segments $PK$ and $QL$ respectively. Prove that $EF$ is parallel to $AB$.
This post has been edited 1 time. Last edited by parmenides51, Aug 16, 2021, 10:29 PM
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OlympusHero
17019 posts
OlympusHero
#2 h  Aug 17, 2021, 4:26 AM
Y by
I'm also not making any progress on this. My only idea was to coordinate bash but the values are very nasty. Can I please have a hint?
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musan1909
45 posts
musan1909
#3 h  Aug 17, 2021, 4:31 AM
Y by
Consider the points $X$ and $Y$ on $AB$ such that $KX$ and $LY$ are perpendicular to $AB$.
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