[/quote]
,
,
,
.
.
: 
-is integer.
of the acute-angled triangle 
is tangent to its side 
at a point 
.
be an altitude of triangle 
be the midpoint of the segment 
is the common point of the circle 
(distinct from 
are tangent to each other at the point 
be the orthocenter of acute triangle 
,
be the foot of the altitude from 
to 
,
be the reflection of 
.
intersects line 
and 
.
.
be the circumcircle of triangle 
.
intersects 
,
is the point on the segment 
.
meets 
.
intersects segments 
,
at 
,
.
be two isogonal conjugate with respect to triangle 
and 
be two points lying on the circle 
such that 
and 
are perpendicular and parallel to bisector of 
and 
bisect two arcs 
and not containing 
.
be a natural number. There are 
and prove 
satisfying 
,
denotes the set of all real numbers.
with integer coefficients such that, for any positive integer 
has an integer root.
,
satisfying the equation 
.
Let 
and 
Show that![\[\sum_{k=1}^n\frac{1}{1+\sum_{j\neq k}x_j}\le\frac n{1+(n-1)\sqrt[n]{x_1x_2\cdots x_n}}.\]](http://latex.artofproblemsolving.com/e/4/c/e4ca07e5003fad8937af3c44dcbc9906fa48e5b4.png)
index this yr (118.5 on amc10+ 9 on AIME) i’m in 7th rn btw first year comp math also. I will grind so hard until like 30 hrs/week. I’m ok at proofs. made mc nats
Y by Pengu14, NaturalSelection, jocaleby1, mynameisjefff, megahertz13, ehuseyinyigit
Hi AOPSers,
I have finished writing a mock geometry test for fun and practice for the real college competitions like HMMT/PUMaC/CMIMC... There would be 10 questions and you should finish the test in 60 minutes, the test would be close to the actual test (hopefully). You could sign up under this thread, PM me your answers!. The submission would close on March 31st at 11:59PM PST.
I would create a private discussion forum so everyone could discuss after finishing the test. This is the first mock I've written, please sign up and enjoy geometry!!
~Bluesoul
Discussion forum: Discussion forum
I have finished writing a mock geometry test for fun and practice for the real college competitions like HMMT/PUMaC/CMIMC... There would be 10 questions and you should finish the test in 60 minutes, the test would be close to the actual test (hopefully). You could sign up under this thread, PM me your answers!. The submission would close on March 31st at 11:59PM PST.
I would create a private discussion forum so everyone could discuss after finishing the test. This is the first mock I've written, please sign up and enjoy geometry!!
~Bluesoul
Discussion forum: Discussion forum
This post has been edited 11 times. Last edited by Bluesoul, 4 hours ago
