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k a May Highlights and 2025 AoPS Online Class Information
jlacosta   0
May 1, 2025
May is an exciting month! National MATHCOUNTS is the second week of May in Washington D.C. and our Founder, Richard Rusczyk will be presenting a seminar, Preparing Strong Math Students for College and Careers, on May 11th.

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[*]May 21st, 4:00pm PT/7:00pm ET, Mathcamp 2025 Qualifying Quiz Part 2 Math Jam, Problems 5 and 6, Canada/USA Mathcamp staff will discuss solutions to Problems 5 and 6 of the 2025 Mathcamp Qualifying Quiz![/list]
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0 replies
jlacosta
May 1, 2025
0 replies
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A Collection of Good Problems from my end
SomeonecoolLovesMaths   20
N 5 minutes ago by AzSolver257
This is a collection of good problems and my respective attempts to solve them. I would like to encourage everyone to post their solutions to these problems, if any. This will not only help others verify theirs but also perhaps bring forward a different approach to the problem. I will constantly try to update the pool of questions.

The difficulty level of these questions vary from AMC 10 to AIME. (Although the main pool of questions were prepared as a mock test for IOQM over the years)

Problem 1

Problem 2

Problem 3

Problem 4

Problem 5
20 replies
SomeonecoolLovesMaths
May 4, 2025
AzSolver257
5 minutes ago
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This shouldn't be a problem 15
derekli   2
N 6 minutes ago by aarush.rachak11
Hey guys I was practicing AIME and came across this problem which is definitely misplaced. It asks for the surface area of a plane within a cylinder which we can easily find out using a projection that is easy to find. I think this should be placed in problem 10 or below. What do you guys think?
2 replies
derekli
2 hours ago
aarush.rachak11
6 minutes ago
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Regular tetrahedron
vanstraelen   7
N 29 minutes ago by ReticulatedPython
Given the points $O(0,0,0),A(1,0,0),B(\frac{1}{2},\frac{\sqrt{3}}{2},0)$
a) Determine the point $C$, above the xy-plane, such that the pyramid $OABC$ is a regular tetrahedron.
b) Calculate the volume.
c) Calculate the radius of the inscribed sphere and the radius of the circumscribed sphere.
7 replies
vanstraelen
May 4, 2025
ReticulatedPython
29 minutes ago
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[ABCD] = n [CDE], areas in trapezoid - IOQM 2020-21 p1
parmenides51   4
N 31 minutes ago by Kizaruno
Let $ABCD$ be a trapezium in which $AB \parallel CD$ and $AB = 3CD$. Let $E$ be then midpoint of the diagonal $BD$. If $[ABCD] = n \times [CDE]$, what is the value of $n$?

(Here $[t]$ denotes the area of the geometrical figure$ t$.)
4 replies
parmenides51
Jan 18, 2021
Kizaruno
31 minutes ago
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No more topics!
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Question abt directed angles
idk12345678   6
N Apr 9, 2025 by idk12345678
If you have a diameter of a circle COA, and there is a point on the circle B, then how do you prove CBA is 90 degrees. Usually, i would use the inscribed angle theorem, but you cant divide directed angles by 2
6 replies
idk12345678
Apr 9, 2025
idk12345678
Apr 9, 2025
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Question abt directed angles
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directed angle
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idk12345678
392 posts
idk12345678
#1 h  Apr 9, 2025, 9:09 PM • 1 Y
Y by PikaPika999
If you have a diameter of a circle COA, and there is a point on the circle B, then how do you prove CBA is 90 degrees. Usually, i would use the inscribed angle theorem, but you cant divide directed angles by 2
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AbhayAttarde01
1486 posts
AbhayAttarde01
#2 h  Apr 9, 2025, 9:53 PM
Y by
for clarification, are the points C, O, and A all on the circle, or is one of them representing the center of the circle
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idk12345678
392 posts
idk12345678
#3 h  Apr 9, 2025, 9:54 PM
Y by
AbhayAttarde01 wrote:
for clarification, are the points C, O, and A all on the circle, or is one of them representing the center of the circle

O is the center
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AbhayAttarde01
1486 posts
AbhayAttarde01
#4 h  Apr 9, 2025, 9:58 PM
Y by
ok and CA is the diameter got it
and wdym by a point on the circle B (like any point on a new circle B)
This post has been edited 1 time. Last edited by AbhayAttarde01, Apr 9, 2025, 9:58 PM
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idk12345678
392 posts
idk12345678
#5 h  Apr 9, 2025, 9:59 PM
Y by
B is on the same circle as C and A
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AbhayAttarde01
1486 posts
AbhayAttarde01
#6 h  Apr 9, 2025, 10:12 PM
Y by
oh ok
well then
the inscribed angle theorem is close, but for when it comes to an angle involving a diameter, it will always be 90
I believe this is called Thale's Threorem, and its a special case for the inscribed angle theorem

but reminder that the angle measure for an inscribed angle is just the measure of the arc divided by 2
This post has been edited 1 time. Last edited by AbhayAttarde01, Apr 9, 2025, 10:16 PM
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idk12345678
392 posts
idk12345678
#7 h  Apr 9, 2025, 10:16 PM
Y by
AbhayAttarde01 wrote:
oh ok
well then
the inscribed angle theorem is close, but for when it comes to an angle involving a diameter, it will always be 90
I believe this is called Thale's Threorem, and its a special case for the inscribed angle theorem

yea, i was asking how does it work with directed angles
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