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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

Are you interested in working towards MATHCOUNTS and don’t know where to start? We have you covered! If you have taken Prealgebra, then you are ready for MATHCOUNTS/AMC 8 Basics. Already aiming for State or National MATHCOUNTS and harder AMC 8 problems? Then our MATHCOUNTS/AMC 8 Advanced course is for you.

Summer camps are starting next month at the Virtual Campus in math and language arts that are 2 - to 4 - weeks in duration. Spaces are still available - don’t miss your chance to have an enriching summer experience. 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 upcoming events:
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[*]May 20th, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 1 Math Jam, Problems 1 to 4, join the Canada/USA Mathcamp staff for this exciting Math Jam, where they discuss solutions to Problems 1 to 4 of the 2025 Mathcamp Qualifying Quiz!
[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
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k i Adding contests to the Contest Collections
dcouchman   1
N Apr 5, 2023 by v_Enhance
Want to help AoPS remain a valuable Olympiad resource? Help us add contests to AoPS's Contest Collections.

Find instructions and a list of contests to add here: https://artofproblemsolving.com/community/c40244h1064480_contests_to_add
1 reply
dcouchman
Sep 9, 2019
v_Enhance
Apr 5, 2023
J
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k i Zero tolerance
ZetaX   49
N May 4, 2019 by NoDealsHere
Source: Use your common sense! (enough is enough)
Some users don't want to learn, some other simply ignore advises.
But please follow the following guideline:


To make it short: ALWAYS USE YOUR COMMON SENSE IF POSTING!
If you don't have common sense, don't post.


More specifically:

For new threads:


a) Good, meaningful title:
The title has to say what the problem is about in best way possible.
If that title occured already, it's definitely bad. And contest names aren't good either.
That's in fact a requirement for being able to search old problems.

Examples:
Bad titles:
- "Hard"/"Medium"/"Easy" (if you find it so cool how hard/easy it is, tell it in the post and use a title that tells us the problem)
- "Number Theory" (hey guy, guess why this forum's named that way¿ and is it the only such problem on earth¿)
- "Fibonacci" (there are millions of Fibonacci problems out there, all posted and named the same...)
- "Chinese TST 2003" (does this say anything about the problem¿)
Good titles:
- "On divisors of a³+2b³+4c³-6abc"
- "Number of solutions to x²+y²=6z²"
- "Fibonacci numbers are never squares"


b) Use search function:
Before posting a "new" problem spend at least two, better five, minutes to look if this problem was posted before. If it was, don't repost it. If you have anything important to say on topic, post it in one of the older threads.
If the thread is locked cause of this, use search function.

Update (by Amir Hossein). The best way to search for two keywords in AoPS is to input
[code]+"first keyword" +"second keyword"[/code]
so that any post containing both strings "first word" and "second form".


c) Good problem statement:
Some recent really bad post was:
[quote]$lim_{n\to 1}^{+\infty}\frac{1}{n}-lnn$[/quote]
It contains no question and no answer.
If you do this, too, you are on the best way to get your thread deleted. Write everything clearly, define where your variables come from (and define the "natural" numbers if used). Additionally read your post at least twice before submitting. After you sent it, read it again and use the Edit-Button if necessary to correct errors.


For answers to already existing threads:


d) Of any interest and with content:
Don't post things that are more trivial than completely obvious. For example, if the question is to solve $x^{3}+y^{3}=z^{3}$, do not answer with "$x=y=z=0$ is a solution" only. Either you post any kind of proof or at least something unexpected (like "$x=1337, y=481, z=42$ is the smallest solution). Someone that does not see that $x=y=z=0$ is a solution of the above without your post is completely wrong here, this is an IMO-level forum.
Similar, posting "I have solved this problem" but not posting anything else is not welcome; it even looks that you just want to show off what a genius you are.

e) Well written and checked answers:
Like c) for new threads, check your solutions at least twice for mistakes. And after sending, read it again and use the Edit-Button if necessary to correct errors.



To repeat it: ALWAYS USE YOUR COMMON SENSE IF POSTING!


Everything definitely out of range of common sense will be locked or deleted (exept for new users having less than about 42 posts, they are newbies and need/get some time to learn).

The above rules will be applied from next monday (5. march of 2007).
Feel free to discuss on this here.
49 replies
ZetaX
Feb 27, 2007
NoDealsHere
May 4, 2019
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Zack likes Moving Points
pinetree1   73
N a minute ago by NumberzAndStuff
Source: USA TSTST 2019 Problem 5
Let $ABC$ be an acute triangle with orthocenter $H$ and circumcircle $\Gamma$. A line through $H$ intersects segments $AB$ and $AC$ at $E$ and $F$, respectively. Let $K$ be the circumcenter of $\triangle AEF$, and suppose line $AK$ intersects $\Gamma$ again at a point $D$. Prove that line $HK$ and the line through $D$ perpendicular to $\overline{BC}$ meet on $\Gamma$.

Gunmay Handa
73 replies
+1 w
pinetree1
Jun 25, 2019
NumberzAndStuff
a minute ago
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Domain and Inequality
Kunihiko_Chikaya   1
N 7 minutes ago by Mathzeus1024
Source: 2018 The University of Tokyo entrance exam / Humanities, Problem 1
Define on a coordinate plane, the parabola $C:y=x^2-3x+4$ and the domain $D:y\geq x^2-3x+4.$
Suppose that two lines $l,\ m$ passing through the origin touch $C$.

(1) Let $A$ be a mobile point on the parabola $C$. Let denote $L,\ M$ the distances between the point $A$ and the lines $l,\ m$ respectively. Find the coordinate of the point $A$ giving the minimum value of $\sqrt{L}+\sqrt{M}.$

(2) Draw the domain of the set of the points $P(p,\ q)$ on a coordinate plane such that for all points $(x,\ y)$ over the domain $D$, the inequality $px+qy\leq 0$ holds.
1 reply
Kunihiko_Chikaya
Feb 25, 2018
Mathzeus1024
7 minutes ago
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JBMO TST Bosnia and Herzegovina 2020 P1
Steve12345   3
N 9 minutes ago by AylyGayypow009
Determine all four-digit numbers $\overline{abcd}$ which are perfect squares and for which the equality holds:
$\overline{ab}=3 \cdot \overline{cd} + 1$.
3 replies
Steve12345
Aug 10, 2020
AylyGayypow009
9 minutes ago
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Problem3
samithayohan   116
N 22 minutes ago by fearsum_fyz
Source: IMO 2015 problem 3
Let $ABC$ be an acute triangle with $AB > AC$. Let $\Gamma $ be its circumcircle, $H$ its orthocenter, and $F$ the foot of the altitude from $A$. Let $M$ be the midpoint of $BC$. Let $Q$ be the point on $\Gamma$ such that $\angle HQA = 90^{\circ}$ and let $K$ be the point on $\Gamma$ such that $\angle HKQ = 90^{\circ}$. Assume that the points $A$, $B$, $C$, $K$ and $Q$ are all different and lie on $\Gamma$ in this order.

Prove that the circumcircles of triangles $KQH$ and $FKM$ are tangent to each other.

Proposed by Ukraine
116 replies
samithayohan
Jul 10, 2015
fearsum_fyz
22 minutes ago
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geometry problem
invt   0
24 minutes ago
In a triangle $ABC$ with $\angle B<\angle C$, denote its incenter and midpoint of $BC$ by $I$, $M$, respectively. Let $C'$ be the reflected point of $C$ wrt $AI$. Let the lines $MC'$ and $CI$ meet at $X$. Suppose that $\angle XAI=\angle XBI=90^{\circ}$. Prove that $\angle C=2\angle B$.
0 replies
invt
24 minutes ago
0 replies
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the locus of $P$
littletush   10
N 33 minutes ago by SuperBarsh
Source: Italy TST 2009 p2
$ABC$ is a triangle in the plane. Find the locus of point $P$ for which $PA,PB,PC$ form a triangle whose area is equal to one third of the area of triangle $ABC$.
10 replies
littletush
Mar 10, 2012
SuperBarsh
33 minutes ago
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Abelkonkurransen 2025 3b
Lil_flip38   3
N 36 minutes ago by Adywastaken
Source: abelkonkurransen
An acute angled triangle \(ABC\) has circumcenter \(O\). The lines \(AO\) and \(BC\) intersect at \(D\), while \(BO\) and \(AC\) intersect at \(E\) and \(CO\) and \(AB\) intersect at \(F\). Show that if the triangles \(ABC\) and \(DEF\) are similar(with vertices in that order), than \(ABC\) is equilateral.
3 replies
Lil_flip38
Mar 20, 2025
Adywastaken
36 minutes ago
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A point on BC
jayme   6
N 44 minutes ago by Captainscrubz
Source: Own ?
Dear Mathlinkers,

1. ABC a triangle
2. 0 the circumcircle
3. D the pole of BC wrt 0
4. B', C' the symmetrics of B, C wrt AC, AB
5. 1b, 1c the circumcircles of the triangles BB'D, CC'D
6. T the second point of intersection of the tangent to 1c at D with 1b.

Prove : B, C and T are collinear.

Sincerely
Jean-Louis
6 replies
jayme
Today at 6:08 AM
Captainscrubz
44 minutes ago
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I got stuck in this combinatorics
artjustinhere237   3
N an hour ago by GreekIdiot
Let $S = \{1, 2, 3, \ldots, k\}$, where $k \geq 4$ is a positive integer.
Prove that there exists a subset of $S$ with exactly $k - 2$ elements such that the sum of its elements is a prime number.
3 replies
artjustinhere237
May 13, 2025
GreekIdiot
an hour ago
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Geo metry
TUAN2k8   5
N an hour ago by Melid
Help me plss!
Given an acute triangle $ABC$. Points $D$ and $E$ lie on segments $AB$ and $AC$, respectively. Lines $BD$ and $CE$ intersect at point $F$. The circumcircles of triangles $BDF$ and $CEF$ intersect at a second point $P$. The circumcircles of triangles $ABC$ and $ADE$ intersect at a second point $Q$. Point $K$ lies on segment $AP$ such that $KQ \perp AQ$. Prove that triangles $\triangle BKD$ and $\triangle CKE$ are similar.
5 replies
TUAN2k8
May 6, 2025
Melid
an hour ago
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power of a point
BekzodMarupov   2
N an hour ago by BekzodMarupov
Source: lemmas in olympiad geometry
Epsilon 1.3. 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.
2 replies
BekzodMarupov
Yesterday at 5:41 AM
BekzodMarupov
an hour ago
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Insspired by Shandong 2025
sqing   3
N an hour ago by JARP091
Source: Own
Let $ a,b,c>0,abc>1$. Prove that$$ \frac {abc(a+b+c+ab+bc+ca+3)}{ abc-1}\geq \frac {81}{4}$$$$ \frac {abc(a+b+c+ab+bc+ca+abc+2)}{ abc-1}\geq 12+8\sqrt{2}$$
3 replies
sqing
3 hours ago
JARP091
an hour ago
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Find the minimum
sqing   4
N 2 hours ago by JARP091
Source: China Shandong High School Mathematics Competition 2025 Q4
Let $ a,b,c>0,abc>1$. Find the minimum value of $ \frac {abc(a+b+c+8)}{abc-1}. $
4 replies
sqing
3 hours ago
JARP091
2 hours ago
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Find (a,n)
shobber   72
N 2 hours ago by Thapakazi
Source: China TST 2006 (1)
Find all positive integer pairs $(a,n)$ such that $\frac{(a+1)^n-a^n}{n}$ is an integer.
72 replies
shobber
Mar 24, 2006
Thapakazi
2 hours ago
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AT=RC [Baltic way 2003]
WakeUp   1
N Nov 7, 2010 by skytin
The diagonals of a cyclic convex quadrilateral $ABCD$ intersect at $P$. A circle through $P$ touches the side $CD$ at its midpoint $M$ and intersects the segments $BD$ and $AC$ again at the points $Q$ and $R$ respectively. Let $S$ be the point on segment $BD$ such that $BS = DQ$. The line through $S$ parallel to $AB$ intersects $AC$ at $T$. Prove that $AT = RC$.
1 reply
WakeUp
Nov 7, 2010
skytin
Nov 7, 2010
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AT=RC [Baltic way 2003]
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geometry
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WakeUp
1347 posts
WakeUp
#1 h  Nov 7, 2010, 2:28 PM • 1 Y
Y by Adventure10
The diagonals of a cyclic convex quadrilateral $ABCD$ intersect at $P$. A circle through $P$ touches the side $CD$ at its midpoint $M$ and intersects the segments $BD$ and $AC$ again at the points $Q$ and $R$ respectively. Let $S$ be the point on segment $BD$ such that $BS = DQ$. The line through $S$ parallel to $AB$ intersects $AC$ at $T$. Prove that $AT = RC$.
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skytin
418 posts
skytin
#2 h  Nov 7, 2010, 4:04 PM • 2 Y
Y by Adventure10, Mango247
Easy to see that AP/PB = DP/PC and CR*CP = DQ*DP = CM*CM , so AT/AP = BS/BP . done
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