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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)!

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[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
0 replies
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Geometry
MathsII-enjoy   0
6 minutes ago
Given triangle $ABC$ inscribed in $(O)$, $S$ is the midpoint of arc $BAC$ of $(O)$. The perpendicular bisector $BO$ intersects $BS$ at $I$. $(I;IB)$ intersects $AB$ at $U$ different from $B$. $H$ is the orthocenter of triangle $ABC$. Prove that $UH$ = $US$
0 replies
MathsII-enjoy
6 minutes ago
0 replies
J
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Find x such that x^4+x^3+x^2+x+1 is perfect square (old)
Amir Hossein   6
N 10 minutes ago by zhoujef000
Find all numbers $x \in \mathbb Z$ for which the number
\[x^4 + x^3 + x^2 + x + 1\]
is a perfect square.
6 replies
Amir Hossein
Oct 3, 2010
zhoujef000
10 minutes ago
J
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Number Theory Chain!
JetFire008   54
N 11 minutes ago by JetFire008
I will post a question and someone has to answer it. Then they have to post a question and someone else will answer it and so on. We can only post questions related to Number Theory and each problem should be more difficult than the previous. Let's start!

Question 1
54 replies
JetFire008
Apr 7, 2025
JetFire008
11 minutes ago
J
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Divisibility NT FE
CHESSR1DER   7
N 17 minutes ago by CHESSR1DER
Source: Own
Find all functions $f$ $N \iff N$ such for any $a,b$:
$(a+b)|a^{f(b)} + b^{f(a)}$.
7 replies
CHESSR1DER
Yesterday at 7:07 PM
CHESSR1DER
17 minutes ago
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No more topics!
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J
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The midpoint of AC is on DE
CatalinBordea   1
N Oct 10, 2018 by sunken rock
Source: Romanian District Olympiad 2017, Grade VII, Problem 4
We have a triangle with $ \angle BAC=\angle BCA. $ The point $ E $ is on the interior bisector of $ \angle ABC $ so that $ \angle EAB =\angle ACB. $ Let $ D $ be a point on $ BC $ such that $ B $ is on the segment $ CD $ (endpoints excluded) and $ BD=AB. $ Show that the midpoint of $ AC $ is on the line $ DE. $
1 reply
CatalinBordea
Oct 10, 2018
sunken rock
Oct 10, 2018
J
The midpoint of AC is on DE
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Reveal topic tags
geometry
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Source: Romanian District Olympiad 2017, Grade VII, Problem 4
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CatalinBordea
2142 posts
CatalinBordea
#1 h  Oct 10, 2018, 6:45 AM • 2 Y
Y by Adventure10, Mango247
We have a triangle with $ \angle BAC=\angle BCA. $ The point $ E $ is on the interior bisector of $ \angle ABC $ so that $ \angle EAB =\angle ACB. $ Let $ D $ be a point on $ BC $ such that $ B $ is on the segment $ CD $ (endpoints excluded) and $ BD=AB. $ Show that the midpoint of $ AC $ is on the line $ DE. $
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sunken rock
4381 posts
sunken rock
#2 h  Oct 10, 2018, 8:22 AM • 2 Y
Y by Adventure10, Mango247
CatalinBordea wrote:
We have a triangle with $ \angle BAC=\angle BCA. $ The point $ E $ is on the interior bisector of $ \angle ABC $ so that $ \angle EAB =\angle ACB. $ Let $ D $ be a point on $ BC $ such that $ B $ is on the segment $ CD $ (endpoints excluded) and $ BD=AB. $ Show that the midpoint of $ AC $ is on the line $ DE. $

As you wrote, $E$ is midpoint of $AC$, hence something wrong!
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