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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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Point satisfies triple property
62861   36
N 15 minutes ago by cursed_tangent1434
Source: USA Winter Team Selection Test #2 for IMO 2018, Problem 2
Let $ABCD$ be a convex cyclic quadrilateral which is not a kite, but whose diagonals are perpendicular and meet at $H$. Denote by $M$ and $N$ the midpoints of $\overline{BC}$ and $\overline{CD}$. Rays $MH$ and $NH$ meet $\overline{AD}$ and $\overline{AB}$ at $S$ and $T$, respectively. Prove that there exists a point $E$, lying outside quadrilateral $ABCD$, such that
[list]
[*] ray $EH$ bisects both angles $\angle BES$, $\angle TED$, and
[*] $\angle BEN = \angle MED$.
[/list]

Proposed by Evan Chen
36 replies
62861
Jan 22, 2018
cursed_tangent1434
15 minutes ago
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Inspired by 2025 Xinjiang
sqing   1
N 21 minutes ago by sqing
Source: Own
Let $ a,b,c >0 . $ Prove that
$$ \left(1+\frac {a} { b}\right)\left(2+\frac {a}{ b}+\frac {b}{ c}\right) \left(1+\frac {a}{b}+\frac {b}{ c}+\frac {c}{ a}\right) \geq 12+8\sqrt 2 $$
1 reply
sqing
Yesterday at 5:32 PM
sqing
21 minutes ago
J
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Inspired by 2025 Beijing
sqing   4
N 29 minutes ago by pooh123
Source: Own
Let $ a,b,c,d >0 $ and $ (a^2+b^2+c^2)(b^2+c^2+d^2)=36. $ Prove that
$$ab^2c^2d \leq 8$$$$a^2bcd^2 \leq 16$$$$ ab^3c^3d \leq \frac{2187}{128}$$$$ a^3bcd^3 \leq \frac{2187}{32}$$
4 replies
sqing
Yesterday at 4:56 PM
pooh123
29 minutes ago
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Find the minimum
sqing   27
N 38 minutes ago by sqing
Source: Zhangyanzong
Let $a,b$ be positive real numbers such that $a^2b^2+\frac{4a}{a+b}=4.$ Find the minimum value of $a+2b.$
27 replies
sqing
Sep 4, 2018
sqing
38 minutes ago
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No more topics!
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computational, circle, BC = CD, <BAC = <DAC
parmenides51   0
Nov 21, 2020
Source: 2008 Belarusian MO B 10.6 (11)
Two adjacent sides of a quadrilateral $ABCD$ are equal, $BC = CD$, and the other two are not, $AB \ne AD$. Also $\angle BAC = \angle DAC$. A circle is drawn through points $A$ and $C$, which intersects for the second time the segment $AB$ at point $N$, and the line $AD$ at point $M$. Find the length of the segment $DM$ if it is known that $BN = a$.
0 replies
parmenides51
Nov 21, 2020
0 replies
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computational, circle, BC = CD, <BAC = <DAC
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Reveal topic tags
geometry
equal angles
equal segments
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Source: 2008 Belarusian MO B 10.6 (11)
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parmenides51
30653 posts
parmenides51
#1 h  Nov 21, 2020, 1:23 PM
Y by
Two adjacent sides of a quadrilateral $ABCD$ are equal, $BC = CD$, and the other two are not, $AB \ne AD$. Also $\angle BAC = \angle DAC$. A circle is drawn through points $A$ and $C$, which intersects for the second time the segment $AB$ at point $N$, and the line $AD$ at point $M$. Find the length of the segment $DM$ if it is known that $BN = a$.
This post has been edited 1 time. Last edited by parmenides51, Nov 21, 2020, 1:28 PM
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