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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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Σ to ∞
phiReKaLk6781   2
N a few seconds ago by P162008
Evaluate: $ \sum\limits_{k=1}^\infty \frac{1}{k\sqrt{k+2}+(k+2)\sqrt{k}}$
2 replies
phiReKaLk6781
Mar 20, 2010
P162008
a few seconds ago
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Challenging Optimization Problem
Shiyul   2
N a few seconds ago by aidan0626
Let $xyz = 1$. Find the minimum and maximum values of $\frac{1}{1 + x + xy}$ + $\frac{1}{1 + y + yz}$ + $\frac{1}{1 + z + zx}$

Can anyone give me a hint? I got that either the minimum or maximum was 1, but I'm sure if I'm correct.
2 replies
Shiyul
4 hours ago
aidan0626
a few seconds ago
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Geometry Angle Chasing
Sid-darth-vater   0
29 minutes ago
Is there a way to do this without drawing obscure auxiliary lines? (the auxiliary lines might not be obscure I might just be calling them obscure)

For example I tried rotating triangle MBC 80 degrees around point C (so the BC line segment would now lie on segment AC) but I couldn't get any results. Any help would be appreciated!
0 replies
+1 w
Sid-darth-vater
29 minutes ago
0 replies
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Number Theory with set and subset and divisibility
SomeonecoolLovesMaths   1
N 2 hours ago by martianrunner
Let $S = \{ 1,2, \cdots, 100 \}$. Let $A$ be a subset of $S$ such that no sum of three distinct elements of $A$ is divisible by $5$. What is the maximum value of $\mid A \mid$.
1 reply
SomeonecoolLovesMaths
3 hours ago
martianrunner
2 hours ago
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PB . CQ = (BC/2)^2, circle related (Rioplatense 2000 L1 p5)
parmenides51   1
N May 7, 2021 by jasperE3
Let $ABC$ be a triangle with $AB = AC$. With center in a point of the side $BC$, the circle $S$ is constructed that is tangent to the sides $AB$ and $AC$. Let $P$ and $Q$ be any points on the sides $AB$ and $AC$ respectively, such that $PQ$ is tangent to $S$. Show that $PB \cdot CQ = \left(\frac{BC}{2}\right)^2$
1 reply
parmenides51
May 18, 2019
jasperE3
May 7, 2021
J
PB . CQ = (BC/2)^2, circle related (Rioplatense 2000 L1 p5)
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tangent
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parmenides51
30630 posts
parmenides51
#1 h  May 18, 2019, 3:43 AM • 2 Y
Y by Adventure10, Mango247
Let $ABC$ be a triangle with $AB = AC$. With center in a point of the side $BC$, the circle $S$ is constructed that is tangent to the sides $AB$ and $AC$. Let $P$ and $Q$ be any points on the sides $AB$ and $AC$ respectively, such that $PQ$ is tangent to $S$. Show that $PB \cdot CQ = \left(\frac{BC}{2}\right)^2$
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jasperE3
11231 posts
jasperE3
#2 h  May 7, 2021, 2:39 PM • 1 Y
Y by parmenides51
https://aops.com/community/p12700760
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