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k a March Highlights and 2025 AoPS Online Class Information
jlacosta   0
Mar 2, 2025
March is the month for State MATHCOUNTS competitions! Kudos to everyone who participated in their local chapter competitions and best of luck to all going to State! Join us on March 11th for a Math Jam devoted to our favorite Chapter competition problems! Are you interested in training for MATHCOUNTS? Be sure to check out our AMC 8/MATHCOUNTS Basics and Advanced courses.

Are you ready to level up with Olympiad training? Registration is open with early bird pricing available for our WOOT programs: MathWOOT (Levels 1 and 2), CodeWOOT, PhysicsWOOT, and ChemWOOT. What is WOOT? WOOT stands for Worldwide Online Olympiad Training and is a 7-month high school math Olympiad preparation and testing program that brings together many of the best students from around the world to learn Olympiad problem solving skills. Classes begin in September!

Do you have plans this summer? There are so many options to fit your schedule and goals whether attending a summer camp or taking online classes, it can be a great break from the routine of the school year. Check out our summer courses at AoPS Online, or if you want a math or language arts class that doesn’t have homework, but is an enriching summer experience, our AoPS Virtual Campus summer camps may be just the ticket! We are expanding our locations for our AoPS Academies across the country with 15 locations so far and new campuses opening in Saratoga CA, Johns Creek GA, and the Upper West Side NY. Check out this page for summer camp information.

Be sure to mark your calendars for the following events:
[list][*]March 5th (Wednesday), 4:30pm PT/7:30pm ET, HCSSiM Math Jam 2025. Amber Verser, Assistant Director of the Hampshire College Summer Studies in Mathematics, will host an information session about HCSSiM, a summer program for high school students.
[*]March 6th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar on Math Competitions from elementary through high school. Join us for an enlightening session that demystifies the world of math competitions and helps you make informed decisions about your contest journey.
[*]March 11th (Tuesday), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS Chapter Discussion MATH JAM. AoPS instructors will discuss some of their favorite problems from the MATHCOUNTS Chapter Competition. All are welcome!
[*]March 13th (Thursday), 4:00pm PT/7:00pm ET, Free Webinar about Summer Camps at the Virtual Campus. Transform your summer into an unforgettable learning adventure! From elementary through high school, we offer dynamic summer camps featuring topics in mathematics, language arts, and competition preparation - all designed to fit your schedule and ignite your passion for learning.[/list]
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0 replies
jlacosta
Mar 2, 2025
0 replies
J
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tangent lines
pnf   1
N 25 minutes ago by ohiorizzler1434
let ABC be a right angel triangle ($\angle A = 90^{\circ}$) and M midpoint of BC. $\omega1$ is the circumcircle of tringle $AMB$ and $\omega2$ circumcircle of triangle $AMC$. the line through C is tangent to $\omega1$ at P and line through B is tangent to $\omega2$ at Q. D is the midpoint of arc BC (does not contain A) in ($ABC$). prove that quadrilateral DPMQ is cyclic.
1 reply
pnf
an hour ago
ohiorizzler1434
25 minutes ago
J
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geometry party
pnf   0
32 minutes ago
https://artofproblemsolving.com/community/c4260013_geometry_party
0 replies
pnf
32 minutes ago
0 replies
J
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Factorial Divisibility
Aryan-23   44
N an hour ago by Ilikeminecraft
Source: IMO SL 2022 N2
Find all positive integers $n>2$ such that
$$ n! \mid \prod_{ p<q\le n, p,q \, \text{primes}} (p+q)$$
44 replies
Aryan-23
Jul 9, 2023
Ilikeminecraft
an hour ago
J
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Prove excircle is tangent to circumcircle
sarjinius   4
N an hour ago by MathLuis
Source: Philippine Mathematical Olympiad 2025 P4
Let $ABC$ be a triangle with incenter $I$, and let $D$ be a point on side $BC$. Points $X$ and $Y$ are chosen on lines $BI$ and $CI$ respectively such that $DXIY$ is a parallelogram. Points $E$ and $F$ are chosen on side $BC$ such that $AX$ and $AY$ are the angle bisectors of angles $\angle BAE$ and $\angle CAF$ respectively. Let $\omega$ be the circle tangent to segment $EF$, the extension of $AE$ past $E$, and the extension of $AF$ past $F$. Prove that $\omega$ is tangent to the circumcircle of triangle $ABC$.
4 replies
sarjinius
Mar 9, 2025
MathLuis
an hour ago
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No more topics!
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Inequality
hiro2023   5
N Today at 1:06 PM by sqing
let a b c is a positive real number
proof that 1/[a(1+b)] + 1/[b(1+c)] + 1/[c(1+a)] >= 3/1+abc
5 replies
hiro2023
Today at 5:22 AM
sqing
Today at 1:06 PM
J
Inequality
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Reveal topic tags
Inequality
inequalities
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G H BBookmark kLocked kLocked NReply
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hiro2023
3 posts
hiro2023
#1 h  Today at 5:22 AM
Y by
let a b c is a positive real number
proof that 1/[a(1+b)] + 1/[b(1+c)] + 1/[c(1+a)] >= 3/1+abc
Z K Y
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removablesingularity
550 posts
removablesingularity
#2 h  Today at 7:40 AM
Y by
Let $a, b, c$ is a positive real number
Prove that $\sum_{cyc}\frac{1}{a\left(1+b\right)} \ge \frac{3}{1+abc}$.
Solution : Note that $\frac{1+abc}{a\left(1+b\right)} = \frac{1+a}{a\left(1+b\right)}+\frac{b\left(1+c\right)}{1+b} - 1$. We have $\sum_{cyc}\frac{1}{a\left(1+b\right)} = \sum_{cyc}\frac{1+a}{a\left(1+b\right)}+\frac{b\left(1+c\right)}{1+b} - 1 \ge 2+2+2-3 = 3$.
Z K Y
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hiro2023
3 posts
hiro2023
#3 h  Today at 7:48 AM
Y by
Could you please proof
(1+a)/[a(1+b)] + [b(1+c)]/1+b >= 2
that would help me a lot :)
Z K Y
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removablesingularity
550 posts
removablesingularity
#4 h  Today at 8:07 AM
Y by
write the other two terms, and strike with am gm
Z K Y
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hiro2023
3 posts
hiro2023
#5 h  Today at 8:16 AM
Y by
OMG thank you so much
I can solve this problem now
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sqing
40985 posts
sqing
#6 h  Today at 1:06 PM
Y by
hiro2023 wrote:
let a b c is a positive real number
proof that 1/[a(1+b)] + 1/[b(1+c)] + 1/[c(1+a)] >= 3/1+abc
Balkan 2006
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