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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
J
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An easiest problem ever
Asilbek777   0
a few seconds ago
Simplify
0 replies
Asilbek777
a few seconds ago
0 replies
J
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Many Reflections form Cyclic
FireBreathers   0
5 minutes ago
Let $ABCD$ be a cyclic quadrilateral. The point $E$ is the reflection of $B$ $w.r.t$ the intersection of $AD$ and $BC$, the point $F$ is the reflection of $B$ $w.r.t$ midpoint of $CD$. Also let $G$ be the reflection of $A$ $w.r.t$ midpoint of $CE$. Show that $C,E,F,G,$ concyclic.
0 replies
FireBreathers
5 minutes ago
0 replies
J
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6 variable inequality
ChuongTk17   4
N 37 minutes ago by arqady
Source: Own
Given real numbers a,b,c,d,e,f in the interval [-1;1] and positive x,y,z,t such that $$2xya+2xzb+2xtc+2yzd+2yte+2ztf=x^2+y^2+z^2+t^2$$. Prove that: $$a+b+c+d+e+f \leq 2$$
4 replies
ChuongTk17
Nov 29, 2024
arqady
37 minutes ago
J
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APMO 2015 P1
aditya21   62
N an hour ago by Tonne
Source: APMO 2015
Let $ABC$ be a triangle, and let $D$ be a point on side $BC$. A line through $D$ intersects side $AB$ at $X$ and ray $AC$ at $Y$ . The circumcircle of triangle $BXD$ intersects the circumcircle $\omega$ of triangle $ABC$ again at point $Z$ distinct from point $B$. The lines $ZD$ and $ZY$ intersect $\omega$ again at $V$ and $W$ respectively.
Prove that $AB = V W$

Proposed by Warut Suksompong, Thailand
62 replies
aditya21
Mar 30, 2015
Tonne
an hour ago
J
No more topics!
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J
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3 midpoints are never collinear
parmenides51   0
Jul 4, 2020
Source: : All-Siberian Open School Olympiad 2014-15 8.4
On the sides of the triangle $AB, BC, AC$ of the triangle $ABC$ in an arbitrary way points $C_1, A_1, B_1$ are selected respectively. Let $K_1, K_2, K_3$ be the midpoints of $AA_1, BB_1, CC_1$. Prove that these points cannot lie on one line
0 replies
parmenides51
Jul 4, 2020
0 replies
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3 midpoints are never collinear
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Reveal topic tags
geometry
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Source: : All-Siberian Open School Olympiad 2014-15 8.4
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parmenides51
30650 posts
parmenides51
#1 h  Jul 4, 2020, 9:59 AM
Y by
On the sides of the triangle $AB, BC, AC$ of the triangle $ABC$ in an arbitrary way points $C_1, A_1, B_1$ are selected respectively. Let $K_1, K_2, K_3$ be the midpoints of $AA_1, BB_1, CC_1$. Prove that these points cannot lie on one line
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