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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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Basic geometry
AlexCenteno2007   6
N 31 minutes ago by vanstraelen
Given an isosceles triangle ABC with AB=BC, the inner bisector of Angle BAC And cut next to it BC in D. A point E is such that AE=DC. The inner bisector of the AED angle cuts to the AB side at the point F. Prove that the angle AFE= angle DFE
6 replies
AlexCenteno2007
Feb 9, 2025
vanstraelen
31 minutes ago
J
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Algebraic Manipulation
Darealzolt   1
N 42 minutes ago by Soupboy0
Find the number of pairs of real numbers $a, b, c$ that satisfy the equation $a^4 + b^4 + c^4 + 1 = 4abc$.
1 reply
Darealzolt
2 hours ago
Soupboy0
42 minutes ago
J
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BrUMO 2025 Team Round Problem 13
lpieleanu   1
N 43 minutes ago by vanstraelen
Let $\omega$ be a circle, and let a line $\ell$ intersect $\omega$ at two points, $P$ and $Q.$ Circles $\omega_1$ and $\omega_2$ are internally tangent to $\omega$ at points $X$ and $Y,$ respectively, and both are tangent to $\ell$ at a common point $D.$ Similarly, circles $\omega_3$ and $\omega_4$ are externally tangent to $\omega$ at $X$ and $Y,$ respectively, and are tangent to $\ell$ at points $E$ and $F,$ respectively.

Given that the radius of $\omega$ is $13,$ the segment $\overline{PQ}$ has a length of $24,$ and $YD=YE,$ find the length of segment $\overline{YF}.$
1 reply
lpieleanu
Apr 27, 2025
vanstraelen
43 minutes ago
J
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Inequlities
sqing   33
N an hour ago by sqing
Let $ a,b,c\geq 0 $ and $ a^2+ab+bc+ca=3 .$ Prove that$$\frac{1}{1+a^2}+ \frac{1}{1+b^2}+ \frac{1}{1+c^2} \geq \frac{3}{2}$$$$\frac{1}{1+a^2}+ \frac{1}{1+b^2}+ \frac{1}{1+c^2}-bc \geq -\frac{3}{2}$$
33 replies
sqing
Jul 19, 2024
sqing
an hour ago
J
No more topics!
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split 90-60-30 ABC, median // angle bisector (2011 Euler Olympiad Remote 4.2)
parmenides51   1
N Feb 11, 2021 by vanstraelen
Divide a $ 30 ^ \circ $ right-angled triangle into two smaller triangles so that some median of one of these triangles is parallel to one of the angle bisectors of the second triangle.
1 reply
parmenides51
Feb 7, 2021
vanstraelen
Feb 11, 2021
J
split 90-60-30 ABC, median // angle bisector (2011 Euler Olympiad Remote 4.2)
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geometry
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parmenides51
30650 posts
parmenides51
#1 h  Feb 7, 2021, 2:56 PM
Y by
Divide a $ 30 ^ \circ $ right-angled triangle into two smaller triangles so that some median of one of these triangles is parallel to one of the angle bisectors of the second triangle.
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vanstraelen
9003 posts
vanstraelen
#2 h  Feb 11, 2021, 10:15 AM
Y by
Let $A(0,0),B(a,0),C(0,\sqrt{3}a)$, then $D(0,\frac{a(\sqrt{3}-1)}{2})$.
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