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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)!

Be sure to mark your calendars for the following events:
[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 9th (Webinar), 4:00pm PT/7:00pm ET, Learn about Video-based Summer Camps at the Virtual Campus
[*]April 10th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MathILy and MathILy-Er Math Jam: Multibackwards Numbers
[*]April 22nd (Webinar), 4:00pm PT/7:00pm ET, Competitive Programming at AoPS (USACO).[/list]
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jlacosta
Apr 2, 2025
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A problem with a rectangle
Raul_S_Baz   7
N 8 minutes ago by undefined-NaN
On the sides AB and AD of the rectangle ABCD, points M and N are taken such that MB = ND. Let P be the intersection of BN and CD, and Q be the intersection of DM and CB. How can we prove that PQ || MN?
IMAGE
7 replies
Raul_S_Baz
Yesterday at 11:13 AM
undefined-NaN
8 minutes ago
J
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Max and min of a/5+b/4+c/3+d/2 under a/4+b/3+c/2+d=1/2 and a^2/7+b^2/5+c^2/3+...
tom-nowy   0
12 minutes ago
Let $a, b, c, d$ be real numbers satisfying the following two conditions:
\begin{align*} &\frac{a}{4}+\frac{b}{3}+\frac{c}{2}+d=\frac{1}{2}, \\ &\frac{a^2}{7}+\frac{b^2}{5}+\frac{c^2}{3}+d^2 + \frac{ab}{3}+\frac{2ac}{5}+\frac{ad}{2} +\frac{bc}{2}+\frac{2bd}{3}+\frac{cd}{2}=\frac{1}{3} . \end{align*}Find the possible maximum and minimum values of
$$\frac{a}{5}+\frac{b}{4}+\frac{c}{3}+\frac{d}{2}.$$
0 replies
tom-nowy
12 minutes ago
0 replies
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Number theory
MathsII-enjoy   1
N 29 minutes ago by anduran
$Find$ $all$ $integers$ $n$ $such$ $that$ $n-1$ $and$ $\frac{n(n+1)}{2}$ $is$ $a$ $perfect$ $number$.
1 reply
MathsII-enjoy
Today at 5:21 AM
anduran
29 minutes ago
J
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equilateral geo 2024 TMC AIME Mock #12
parmenides51   2
N an hour ago by mathafou
Let $ABC$ be an equilateral triangle. Let $D$ be a point on $AB$, $E$ be a point on $BC$, and $F$ be a point on $AC$ such that $\angle DEF = 120^o$ and̸ $\angle DFE = 30^o$. If $AB = 108$ and $CF = 38$, find $AD$.
2 replies
parmenides51
Yesterday at 8:15 PM
mathafou
an hour ago
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AD+BC>=CD, <DMC=90^o, AM=//MB (2015 Math. Multiathlon Reggata J 2.2)
parmenides51   0
Mar 21, 2021
In a quadrilateral $ABCD$, point $M$ is the midpoint of side $AB$. Prove that if the angle $DMC$ is right , then $AD+BC \ge CD .$
0 replies
parmenides51
Mar 21, 2021
0 replies
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AD+BC>=CD, <DMC=90^o, AM=//MB (2015 Math. Multiathlon Reggata J 2.2)
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parmenides51
#1 h  Mar 21, 2021, 11:06 PM
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In a quadrilateral $ABCD$, point $M$ is the midpoint of side $AB$. Prove that if the angle $DMC$ is right , then $AD+BC \ge CD .$
This post has been edited 1 time. Last edited by parmenides51, Mar 22, 2021, 1:05 AM
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