[/quote]
,
and 
be positive integers, and let 
be a 
grid of unit squares.
or 
rectangle. A subset 
of grid squares in 
edges of the grid squares.
,
,
,
be non-negative real numbers such that![\[2a+2b+2c+2d+ab+bc+cd+da+3=abcd.\]](http://latex.artofproblemsolving.com/d/e/8/de8ccd816cfe032a97d940982192b1abea21dc18.png)
prove that : ![\[\sqrt[4]{abc}+\sqrt[4]{bcd}+\sqrt[4]{cda}+\sqrt[4]{dab}\le\sqrt[4]{27(1+a)(1+b)(1+c)(1+d)}.\]](http://latex.artofproblemsolving.com/a/f/c/afc556cd8f5c7f4dedf153ffb92fb1f978c56823.png)
be a triangle, with incenter 
and 
-
.
,
,
and 
intersect the circumcircle of 
,
,
and 
,
be diameters in the circumcircles of triangles 
and 
respectively.
.
and 
Prove that
Where 
Where 
.
and 
are on 
and 
respectively such that 
.
and 
meet at 
.
and 
is the orthocenter of 
.
and 
are circles with diameter 
and 
,
and 
.
.
.
satisfying:
and 
are externally tangent at a point 
be a line tangent to 
and 
.
and 
be diameters in 
and 
are tangent to 
and 
are tangent to 
.
,
times the radius of 
and 
are chosen on 
,
is the foot of the altitude from 
.
are similarly defined, prove that lines 
and 
concurr on 
.
and let 
and 
,
and 
and 
.
,
and 
,
.
and 
be feet of perpendiculars from 
and 
respectively. Prove that 
,
and 
are concurrent.
.
is a sequence of integers satisfying 
,
,
,
Prove that there exists 
such that 
.
and 
,
.
,
is composite, then all positive divisors of 
Y by
Hello! I am a 6th grader this year about to become 7th grade next year. I was wondering if I should take the AMC 12 next year because I think I am ready for it, I was thinking to do AMC 10 A and AMC 12 B, do you think it is a good idea? Here are the courses I finished and now I am working on:
Finished:
1. Intro Algebra
2. Intro Number Theory
3. Intro Counting and Probability
4. Volume 1
Working on:
1. Intermdiate Counting and Probability
2. Three Year Mathcounts Marathon
Upcoming:
1. Intro Geomtery (Next Month)
2. Intro to Alg (May)
3. Pre-calc (Summer)
4. Volume 2???
Stats for AMC 12 (Mocked):
1. AMC 12 A 2024: 100.5
2. AMC 12 B 2024: 105
3. AMC 12 A 2023: 96
The reason why I sometimes I get 100+ is because sometimes I know how to do the first step of the problem but the last step I have to kind of infrence but still i know how to do the problem.
Finished:
1. Intro Algebra
2. Intro Number Theory
3. Intro Counting and Probability
4. Volume 1
Working on:
1. Intermdiate Counting and Probability
2. Three Year Mathcounts Marathon
Upcoming:
1. Intro Geomtery (Next Month)
2. Intro to Alg (May)
3. Pre-calc (Summer)
4. Volume 2???
Stats for AMC 12 (Mocked):
1. AMC 12 A 2024: 100.5
2. AMC 12 B 2024: 105
3. AMC 12 A 2023: 96
The reason why I sometimes I get 100+ is because sometimes I know how to do the first step of the problem but the last step I have to kind of infrence but still i know how to do the problem.
This post has been edited 2 times. Last edited by sadas123, Mar 18, 2025, 5:15 PM
