[/quote]
,
,
lies on side 
and point 
lies on side 
.
and 
be points on segments 
and 
,
is parallel to 
.
be a point on line 
,
.
be the point on line 
,
.
,
be the circumcircle of a triangle 
.
and 
meets the sides 
and 
at 
and 
,
and 
meet 
and 
,
at 
and 
,
and 
meet at 
is the orthocenter of an acute triangle 
be the midpoint of 
meets 
respectively. 
meets 
at 
at 
are collinear.
prime number, there exists only one positive number 
that makes the equation 
a perfect square of a positive integer
be a real-valued function defined on the set of real numbers that satisfies![\[f(x + y) \leq yf(x) + f(f(x))\]](http://latex.artofproblemsolving.com/c/9/4/c94075d26e09712f5393fb66ecbfdc2573c239b6.png)
and 
.
for all 
.
,
.
and the external angle bisector of 
and 
,
,
.
be an acute triangle, and let 
and 
,
and 
lie on lines 
and 
(where 
)
is a parallelogram. Prove that![\[\frac{OQ_{1}}{OP_{1}}+\frac{OQ_{2}}{OP_{2}}+\frac{OQ_{3}}{OP_{3}}\geq 3.\]](http://latex.artofproblemsolving.com/b/a/5/ba563336236b6a04fc9ef661760fa1251bfb07d6.png)
.
in this order. Prove that![\[a_1a_3+a_3a_5+a_5a_7+a_7a_9+a_9a_1=a_2a_4+a_4a_6+a_6a_8+a_8a_{10}+a_{10}a_2.\]](http://latex.artofproblemsolving.com/9/e/e/9ee73bbdc4b4f2cad2eb3fcfb3dbdf76b6200b4d.png)
Y by
Hi,
I just received my USAJMO score distribution: 000 701 (very cursed I know)
The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
I just received my USAJMO score distribution: 000 701 (very cursed I know)
The thing is, I solved #5 (Geometry) by using Cartesian coordinates and tried to show a lot of detail in my calculations. I don't think I mislabeled the pages or anything either. I don't have the scans, but does anyone know why this might be the case? Thank you!
