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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 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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(help urgent) Classic Geo Problem / Angle Chasing?
orangesyrup   2
N 7 minutes ago by imnotgoodatmathsorry
Source: own
In the given figure, ABC is an isosceles triangle with AB = AC and ∠BAC = 78°. Point D is chosen inside the triangle such that AD=DC. Find the measure of angle X (∠BDC).

ps: see the attachment for figure
2 replies
+2 w
orangesyrup
40 minutes ago
imnotgoodatmathsorry
7 minutes ago
J
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Interesting combinatoric problem on rectangles
jaydenkaka   0
9 minutes ago
Source: Own
Define act <Castle> as following:
For rectangle with dimensions i * j, doing <Castle> means to change its dimensions to (i+p) * (j+q) where p,q is a natural number smaller than 3.

Define 1*1 rectangle as "C0" rectangle, and define "Cn" ("n" is a natural number) as a rectangle that can be created with "n" <Castle>s.
Plus, there is a constraint for "Cn" rectangle. The constraint is that "Cn" rectangle's area must be bigger than n^2 and be same or smaller than (n+1)^2. (n^2 < Area =< (n+1)^2)

Let all "C20" rectangle's area's sum be A, and let all "C20" rectangles perimeter's sum be B.
What is A-B?
0 replies
jaydenkaka
9 minutes ago
0 replies
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Collect ...
luutrongphuc   2
N 29 minutes ago by megarnie
Find all functions $f: \mathbb{R^+} \rightarrow \mathbb{R^+}$ such that:
$$f\left(f(xy)+1\right)=xf\left(x+f(y)\right)$$
2 replies
luutrongphuc
Apr 21, 2025
megarnie
29 minutes ago
J
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hard problem
Cobedangiu   8
N 39 minutes ago by IceyCold
Let $x,y,z>0$ and $xy+yz+zx=3$ : Prove that :
$\sum \ \frac{x}{y+z}\ge\sum \frac{1}{\sqrt{x+3}}$
8 replies
Cobedangiu
Apr 2, 2025
IceyCold
39 minutes ago
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No more topics!
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angle chasing , <BAC = 60^o , 2 < BAE = <ACB
parmenides51   1
N Oct 21, 2023 by sunken rock
Source: Switzerland - Swiss MO 2016 p1
Let $ABC$ be a triangle with $\angle BAC = 60^o$. Let $E$ be the point on the side $BC$ , such that $2 \angle BAE = \angle ACB$ . Let $D$ be the second intersection of $AB$ and the circumcircle of the triangle $AEC$ and $P$ be the second intersection of $CD$ and the circumcircle of the triangle $DBE$. Calculate the angle $\angle BAP$.
1 reply
parmenides51
Jul 15, 2020
sunken rock
Oct 21, 2023
J
angle chasing , <BAC = 60^o , 2 < BAE = <ACB
G H J
Reveal topic tags
angles
geometry
equal angles
circumcircle
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G H BBookmark kLocked kLocked NReply
Source: Switzerland - Swiss MO 2016 p1
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parmenides51
30630 posts
parmenides51
#1 h  Jul 15, 2020, 5:53 PM • 3 Y
Y by Mango247, Mango247, Rounak_iitr
Let $ABC$ be a triangle with $\angle BAC = 60^o$. Let $E$ be the point on the side $BC$ , such that $2 \angle BAE = \angle ACB$ . Let $D$ be the second intersection of $AB$ and the circumcircle of the triangle $AEC$ and $P$ be the second intersection of $CD$ and the circumcircle of the triangle $DBE$. Calculate the angle $\angle BAP$.
This post has been edited 1 time. Last edited by parmenides51, Jul 16, 2020, 8:27 PM
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sunken rock
4384 posts
sunken rock
#2 h  Oct 21, 2023, 11:44 AM
Y by
hint.

Best regards,
sunken rock
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