[/quote]
,
![\[ \begin{tabular}{c c c c}
{} & \textbf{Adams} & \textbf{Baker} & \textbf{Adams and Baker} \\
\textbf{Boys:} & 71 & 81 & 79 \\
\textbf{Girls:} & 76 & 90 & ? \\
\textbf{Boys and Girls:} & 74 & 84 & \\
\end{tabular}
\]](http://latex.artofproblemsolving.com/8/5/c/85c75770c3f90af49df0db600dead2a29e6674b3.png)
be an isosceles trapezoid with 
.
of triangle 
meets 
at 
.
be a point on the (internal) angle bisector of 
such that 
.
meet line 
and 
.
is isosceles.
such that, for all positive integers 
and 
,
be real numbers so that 
and 
Show that
inscribed in a circle 
with center 
.
the incenter of triangle 
the contact points of the incircle with sides 
of triangle 
the foot of the perpendicular line from 
to the line 
.
passes from the antidiametric point 
of 
in the circle 
is a diametre of the circle 
play a game in which they take turns choosing positive integers 
.
and 
,
and 
.
and internally tangent to 
.
and 
intersect at a point lying on 
grid, two cells are considered neighboring if they share a common edge. Kritesh performs the following actions:
in any cell of the grid.
.
be non-negative real numbers such that 
Prove that
,
be the orthocenter of 
.
at 
at 
be the midpoint of 
,
meet 
.
at 
.
is tangent to 
Y by jh235, SteveLi, epiclucario, DrMath, somepersonoverhere, stan23456, TheMaskedMagician, droid347, miru99, spartan168, Einstein314, checkmatetang, rjiang16, Benq, PlatinumFalcon, Adventure10, and 7 other users
I made a Mock AMC 10/12. It leans more towards the 10, but can still be great preparation for the 12. Because I want everybody to have a chance at the problem, I tried to limit the trig. I will probably release it tomorrow and run the due date through the 20th (of February). Please no sign-ups, just submit your answers to me by February 20th at 8 PM EST. I will probably get results back on the 21st and I will release the answers immediately. I have the contest made, I just need to make sure all of my answers are right and that there are no grammatical errors. Other than that I'll probably post it tomorrow at 6 PM.
Oh, and one more thing. I'll have a Mock AIME around early-mid March. That will be harder than usual to make up for difficulty to the people on the 12.
EDIT: Here's the link: https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0
Errata: number 24: the diagonals aren't integers and you should find a+b+c given the area is a(rtb)/c. A. 20 B. 70 C. 120 D. 220 E. 270
Oh, and one more thing. I'll have a Mock AIME around early-mid March. That will be harder than usual to make up for difficulty to the people on the 12.
EDIT: Here's the link: https://www.dropbox.com/s/1c8hhl6yt2awpix/Mock%20AMC%2010.pdf?dl=0
Errata: number 24: the diagonals aren't integers and you should find a+b+c given the area is a(rtb)/c. A. 20 B. 70 C. 120 D. 220 E. 270
This post has been edited 4 times. Last edited by joey8189681, Feb 12, 2015, 2:24 AM
up. (this is why i shouldn't forum)
(it's way better than my derped 10a score, so I feel good)
