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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
[*]April 8th (Math Jam), 4:30pm PT/7:30pm ET, 2025 MATHCOUNTS State Discussion
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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0 replies
jlacosta
Apr 2, 2025
0 replies
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Inequalities
sqing   3
N 3 minutes ago by sqing
Let $a,b$ be real numbers such that $ a^2+b^2+a^3 +b^3=4 . $ Prove that
$$a+b \leq 2$$Let $a,b$ be real numbers such that $a+b + a^2+b^2+a^3 +b^3=6 . $ Prove that
$$a+b \leq 2$$
3 replies
sqing
Saturday at 1:10 PM
sqing
3 minutes ago
J
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Congruence
Ecrin_eren   3
N 36 minutes ago by lbh_qys
Find the number of integer pairs (x, y) satisfying the congruence equation:

3y² + 3x²y + y³ ≡ 3x² (mod 41)

for 0 ≤ x, y < 41.

3 replies
Ecrin_eren
Apr 3, 2025
lbh_qys
36 minutes ago
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Problem nt
HopefullyMcNats2025   2
N 2 hours ago by mathnerd_101
How many positive integers from 1-100000 fit the conditions, they are not divisble by 3, 5, or 8 and that they are palindromes,
2 replies
HopefullyMcNats2025
Yesterday at 7:27 PM
mathnerd_101
2 hours ago
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Eazy equation clap
giangtruong13   1
N 6 hours ago by iniffur
Find all $x,y,z$ satisfy that: $$\frac{x}{y+z}=2x-1; \frac{y}{x+z}=3y-1;\frac{z}{x+y}=5z-1$$
1 reply
giangtruong13
Saturday at 4:03 PM
iniffur
6 hours ago
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OI _|_ A-bisector when BC=(AB+AC)/2 (Mathematical Excalibur 383)
parmenides51   1
N Apr 2, 2020 by DarthVader2618
Let $O$ and $I$ be the circumcenter and incenter of $\triangle ABC$ respectively. If $AB\ne AC$, points $D, E$ are midpoints of $AB, AC$ respectively and $BC=(AB+AC)/2$, then prove that the line $OI$ and the bisector of $\angle CAB$ are perpendicular .
1 reply
parmenides51
Apr 2, 2020
DarthVader2618
Apr 2, 2020
J
OI _|_ A-bisector when BC=(AB+AC)/2 (Mathematical Excalibur 383)
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Reveal topic tags
geometry
Circumcenter
incenter
angle bisector
perpendicular
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parmenides51
30629 posts
parmenides51
#1 h  Apr 2, 2020, 4:09 PM
Y by
Let $O$ and $I$ be the circumcenter and incenter of $\triangle ABC$ respectively. If $AB\ne AC$, points $D, E$ are midpoints of $AB, AC$ respectively and $BC=(AB+AC)/2$, then prove that the line $OI$ and the bisector of $\angle CAB$ are perpendicular .
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DarthVader2618
20 posts
DarthVader2618
#2 h  Apr 2, 2020, 7:04 PM
Y by
solution
This post has been edited 1 time. Last edited by DarthVader2618, Apr 2, 2020, 8:34 PM
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