geometry problem
by kjhgyuio, Apr 20, 2025, 10:21 PM
Attachments:
2024 MathCounts Nationals Target #2
by UberPiggy, Apr 19, 2025, 11:32 PM
I know target #2 is supposed to be easy but I literally cannot figure out how to do this one. Could someone help please?
Trapezoid
has parallel bases 
and 
, 
is the midpoint of side 
and 
. If 
cm and 
cm, what is 
? Express your answer in simplest radical form.
The answer is
This came with a diagram but I'm too lazy to attach it here
Trapezoid
has parallel bases 
and 
, 
is the midpoint of side 
and 
. If 
cm and 
cm, what is 
? Express your answer in simplest radical form.The answer is
This came with a diagram but I'm too lazy to attach it here
Weird Similarity
by mithu542, Apr 18, 2025, 6:03 PM
Is it just me or are the 2023 national sprint #21 and 2025 state target #4 strangely similar?
2023 Natioinal Sprint #21 wrote:
A right triangle with integer side lengths has perimeter 
feet and area ft^2. What is the arithmetic mean of all possible values of ?
feet and area ft^2. What is the arithmetic mean of all possible values of ?2025 State Target #4 wrote:
Suppose a right triangle has an area of 20 cm^2 and a perimeter of 40 cm. What is
the length of the hypotenuse, in centimeters?
the length of the hypotenuse, in centimeters?
This post has been edited 2 times. Last edited by mithu542, Apr 18, 2025, 6:04 PM
Geometry Transformation Problems
by ReticulatedPython, Apr 17, 2025, 3:46 PM
Problem 1:
A regular hexagon of side length
is rotated 
degrees about one side. The space through which the hexagon travels during the rotation forms a solid. Find the volume of this solid.
Problem 2:
A regular octagon of side length is rotated degrees about one side. The space through which the octagon travels through during the rotation forms a solid. Find the volume of this solid.
Source:Own
A regular hexagon of side length
is rotated 
degrees about one side. The space through which the hexagon travels during the rotation forms a solid. Find the volume of this solid.Problem 2:
A regular octagon of side length
is rotated degrees about one side. The space through which the octagon travels through during the rotation forms a solid. Find the volume of this solid.Source:Own
and height 
:
Volume of cone frustum with base radii 
,
This post has been edited 11 times. Last edited by ReticulatedPython, Apr 21, 2025, 3:33 PM
A geometry problem
by Deomad123, Apr 8, 2025, 7:20 PM
Let be an cyclic quadrilateral with 
,
,
and 
Find:
be an cyclic quadrilateral with 
,
,
and 
Find:
1000th Post!
by PikaPika999, Apr 5, 2025, 11:32 PM
When I had less than 25 posts on AoPS, I saw many people create threads about them getting 1000th posts. I thought I would never hit 1000 posts, but here we are, this is my 1000th post.
As a lot of users like to do, I'll write my math story:
In conclusion, AoPS has helped me improve my math. I have also made many new friends on AoPS!
Finally, I would like to say thank you to all the new friends I made and all the instructors on AoPS that taught me!
As a lot of users like to do, I'll write my math story:
In conclusion, AoPS has helped me improve my math. I have also made many new friends on AoPS!
Finally, I would like to say thank you to all the new friends I made and all the instructors on AoPS that taught me!
,![[asy]draw((0,0)--(4,0)--(4,9)--(-2,9)--(-2,4)--(0,4)--cycle);
label("A",(-2,9),NW);
label("B",(4,9),NE);
label("C",(4,0),SE);
label("D",(0,0),SW);
label("E",(0,4),NE);
label("F",(-2,4),SW);
label("5",(-2,6.5),W);
label("4",(2,0),S);
label("9",(4,4.5),E);
label("6",(1,9),N);
label("All angles in this diagram are right.",(0,-3),S);[/asy]](http://latex.artofproblemsolving.com/0/5/0/05066364c4db136187194d2e2aefd14b3f7e0b08.png)
![\[ \textbf{(A)}\ 24 \qquad
\textbf{(B)}\ 30 \qquad
\textbf{(C)}\ 46 \qquad
\textbf{(D)}\ 66 \qquad
\textbf{(E)}\ 74
\]](http://latex.artofproblemsolving.com/8/2/f/82ffc15072ca99f6cd1abc312781eb4827817356.png)
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