[/quote]
,
be triangle, inscribed in parabola. Tangents in points 
forms triangle 
.
.
)
such that there exist integers 
with ![\[x^3_1+x^3_2+\,\ldots\,+x^3_t=2002^{2002}\,?\]](http://latex.artofproblemsolving.com/e/f/a/efaa98e77ac0273284ee3446e4335d8cc4f681cb.png)
and 
doubloons, where 
.
is called lucky if the sum in 
coins. Find the number of lucky numbers.
with no parallel sides is inscribed in a circle 
.
are inscribed in triangles 
,
and 
,
,
,
.
be a quadrilateral inscribed in a circle 
such that 
.
and 
be the midpoints of 
and 
respectively. The line 
meets 
.
are concurrent.
be a continuous function. A chord is defined as a segment of integer length, parallel to the x-axis, whose endpoints lie on the graph of 
.
chords, one of which has length 2025. Find the minimum possible value of 
has been partitioned into disjoint pairs 
)
,
equals 
or 
.![\[ |a_1-b_1|+|a_2-b_2|+\cdots +|a_{999}-b_{999}| \]](http://latex.artofproblemsolving.com/0/4/4/04422a7d2266b92a6b3f215b698f078cda85091f.png)
ends in the digit 
.
.
and also tangent to 
at 
.
intersect 
and 
respectively. Let 
is the midpoint of 
and 
is the midpoint of 
.
and 
meet at 
and intersect 
and 
respectively. The ray 
meets the circumcircle of triangle 
again at 
.
.
(i dont remember exactly if it was 8032038 or some other number, so correct me on this)
(i posted this at 12:29) lol
?
its circumcentre. A line tangent to the circumcircle of the triangle 
intersects sides 
be the image of 
.
is tangent to the circumcircle of triangle 
be a semicircle with diameter 
touches 
in a point 
touches 
and 
and 
are perpendicular.
Y by RainbowJessa, cubres, At777
I believe discussion is allowed after yesterday at midnight, correct?
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag
If so, I will put tentative answers on this thread.
By the way, does anyone know the answer to Geometry Problem 5? I was wondering if I got that one right
Also, if you put answers, please put it in a hide tag
This post has been edited 21 times. Last edited by Aaronjudgeisgoat, Yesterday at 11:32 AM
minutes to solve it.
game using the integers 
exactly once"
