[/quote]
,
be an acute scalene triangle. A point 
varies on its side 
.
and 
are the midpoints of the arcs 
and 
(not containing 
and 
,
passes through a fixed point, independent of the choice of 
such that 
divides 
for any positive integers 
and 
.
be an acute scalene triangle inscribed in a circle 
.
intersects 
and 
.
is the midpoint of 
.
be the altitude in 
,
intersects 
be the midpoint of 
be the reflection of 
and 
are similar.
and 
Prove that 
and 
.
Prove 
Find maximum 
that is not isosceles at 
,
be its incircle, which is tangent to 
at 
,
and 
intersect the line passing through 
at 
and 
,
and perpendicular to 
intersect 
and 
at 
and 
,
are collinear and that 
are concurrent.
,
.
such that 
.
corresponds to 
)
be non-negative real numbers such that 
Prove that
,
,
,
,
.
Y by
I missed the signup for MATHCOUNTS this year, and I think I could have made it to nats, based on my scores on the tests(I took them after MATHCOUNTS posted them on their website). Anyone have any study tips for next year?
P.S. Does anybody know if you can sign up for MATHCOUNTS individually, or do I need to try to convince 3 other kids from my school to compete?
P.S. Does anybody know if you can sign up for MATHCOUNTS individually, or do I need to try to convince 3 other kids from my school to compete?
