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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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Problem 6
blug   1
N an hour ago by atdaotlohbh
Source: Polish Math Olympiad 2025 Finals P6
A strictly decreasing function $f:(0, \infty)\Rightarrow (0, \infty)$ attaining all positive values and positive numbers $a_1\ne b_1$ are given. Numbers $a_2, b_2, a_3, b_3, ...$ satisfy
$$a_{n+1}=a_n+f(b_n),\;\;\;\;\;\;\;b_{n+1}=b_n+f(a_n)$$for every $n\geq 1$. Prove that there exists a positive integer $n$ satisfying $|a_n-b_n| >2025$.
1 reply
blug
Yesterday at 12:17 PM
atdaotlohbh
an hour ago
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Regarding Maaths olympiad prepration
omega2007   13
N an hour ago by omega2007
<Hey Everyone'>
I'm 10 grader student and Im starting prepration for maths olympiad..>>> From scratch (not 2+2=4 )

Do you haves compiled resources of Handouts,
PDF,
Links,
List of books topic wise
which are shared on AOPS (and from your perspective) for maths olympiad and any useful thing, which will help me in boosting Maths olympiad prepration.
13 replies
omega2007
Yesterday at 3:13 PM
omega2007
an hour ago
J
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square root problem that involves geometry
kjhgyuio   5
N an hour ago by kjhgyuio
If x is a nonnegative real number , find the minimum value of √x^2+4 + √x^2 -24x +153

5 replies
kjhgyuio
Today at 3:56 AM
kjhgyuio
an hour ago
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PoP+Parallel
Solilin   3
N an hour ago by ND_
Source: Titu Andreescu, Lemmas in Olympiad Geometry
Let ABC be a triangle and let D, E, F be the feet of the altitudes, with D on BC, E on CA, and F on AB. Let the parallel through D to EF meet AB at X and AC at Y. Let T be the intersection of EF with BC and let M be the midpoint of side BC. Prove that the points T, M, X, Y are concyclic.
3 replies
Solilin
5 hours ago
ND_
an hour ago
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No more topics!
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KNMP # if KP _|_ AC and KN _|_ BC, 2 altitudes, circumcenter
parmenides51   0
Jun 29, 2022
Source: 2005 Rusanovsky Lyceum Olympiad p117
Let the point $O$ be the center of the circumcircle of the acute-angled triangle $ABC$, and let the segment $CK$ be the altitude of this triangle. On the sides $AC$ and $BC$, the following points $P$ and $N$ are marked, respectively, that $KP \perp AC$ and $KN \perp BC$. The altitude $PL$ of the triangle $PNC$ intersects the line $OC$ at the point $M$. Prove that the quadrilateral $KNMP$ is a parallelogram.
0 replies
parmenides51
Jun 29, 2022
0 replies
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KNMP # if KP _|_ AC and KN _|_ BC, 2 altitudes, circumcenter
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Source: 2005 Rusanovsky Lyceum Olympiad p117
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parmenides51
30629 posts
parmenides51
#1 h  Jun 29, 2022, 12:43 PM
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Let the point $O$ be the center of the circumcircle of the acute-angled triangle $ABC$, and let the segment $CK$ be the altitude of this triangle. On the sides $AC$ and $BC$, the following points $P$ and $N$ are marked, respectively, that $KP \perp AC$ and $KN \perp BC$. The altitude $PL$ of the triangle $PNC$ intersects the line $OC$ at the point $M$. Prove that the quadrilateral $KNMP$ is a parallelogram.
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