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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:
[list][*]May 9th, 4:30pm PT/7:30pm ET, Casework 2: Overwhelming Evidence — A Text Adventure, a game where participants will work together to navigate the map, solve puzzles, and win! All are welcome.
[*]May 19th, 4:30pm PT/7:30pm ET, What's Next After Beast Academy?, designed for students finishing Beast Academy and ready for Prealgebra 1.
[*]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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Inequality
Sadigly   3
N an hour ago by pooh123
Source: Azerbaijan Junior MO 2025 P5
For positive real numbers $x;y;z$ satisfying $0<x,y,z<2$, find the biggest value the following equation could acquire:


$$(2x-yz)(2y-zx)(2z-xy)$$
3 replies
Sadigly
Friday at 7:59 AM
pooh123
an hour ago
J
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Calculus
youochange   2
N an hour ago by youochange
Find the area enclosed by the curves $e^x,e^{-x},x^2+y^2=1$
2 replies
youochange
Yesterday at 2:38 PM
youochange
an hour ago
J
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A strong inequality problem
hn111009   0
an hour ago
Source: Somewhere
Let $a,b,c$ be the positive number satisfied $a^2+b^2+c^2=3.$ Find the minimum of $$P=\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}+\dfrac{3abc}{2(ab+bc+ca)}.$$
0 replies
hn111009
an hour ago
0 replies
J
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help me please,thanks
tnhan.129   0
an hour ago
find f: R+ -> R such that:
f(x)/x + f(y)/y = (1/x + 1/y).f(sqrt(xy))
0 replies
tnhan.129
an hour ago
0 replies
J
No more topics!
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J
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Mixtilinear Excircle Problem
YaoAOPS   1
N Apr 9, 2025 by mriceman
Source: Michael Ren
Let $\triangle ABC$ be a triangle with $A$-mixtilinear incircle $\omega$, and let the tangents from $B$ and $C$ to $\omega$ different from $AB$ and $AC$ meet the circumcircle again at $P$ and $Q$, and let $AP$ and $AQ$ meet $BC$ again at $X$ and $Y$. Show that the $A$-excircle of $\triangle AXY$ is tangent to the circumcircle.
1 reply
YaoAOPS
Apr 8, 2025
mriceman
Apr 9, 2025
J
Mixtilinear Excircle Problem
G H J
Reveal topic tags
geometry
Poncelet Porism
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G H BBookmark kLocked kLocked NReply
Source: Michael Ren
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YaoAOPS
1541 posts
YaoAOPS
#1 h  Apr 8, 2025, 8:33 AM
Y by
Let $\triangle ABC$ be a triangle with $A$-mixtilinear incircle $\omega$, and let the tangents from $B$ and $C$ to $\omega$ different from $AB$ and $AC$ meet the circumcircle again at $P$ and $Q$, and let $AP$ and $AQ$ meet $BC$ again at $X$ and $Y$. Show that the $A$-excircle of $\triangle AXY$ is tangent to the circumcircle.
Z K Y
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mriceman
3 posts
mriceman
#2 h  Apr 9, 2025, 2:48 PM
Y by
Great problem, this is my sketch of the solution.
Attachments:
This post has been edited 2 times. Last edited by mriceman, Apr 9, 2025, 2:48 PM
Reason: oh
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