to be an infinite polynomial where ![\[P(x) = \lim_{n\to \infty}\prod_{k=0}^n \left(x-\left(\cos\left(\dfrac{2\pi k}{n}\right)+i\sin\left(\dfrac{2\pi k}{n}\right)\right)\right).\]](http://latex.artofproblemsolving.com/c/a/8/ca8d0747b7186eb097eb7bd71a95f75d2e38af32.png)
,
.
,
terms. 
be real numbers with 
that satisfy the equations
}
,
,
are positive integers. What is 
?
to 
.
,
,
and performs that operation on them. Find the expected value of the answer.
has a right angle at 
.
and 
.
lies on 
such that 
and point 
lies on 
such that 
= 
.
.
.
.
.
.
.
from base 
shares angles 
with 
through AA Postulate. 
,
and 
.
,
(as both are right angles), and 
,
through SAS postulate. 
,
.
.
Y by
Given a circle with center 
, and square 
. Point 
and 
are on the circle, and 
is tangent to the circle at point 
. Let 
represent the midpoint of 
and 
represent the intersection between and circle. Prove that 
.
, and square 
. Point 
and 
are on the circle, and 
is tangent to the circle at point 
. Let 
represent the midpoint of 
and 
represent the intersection between and circle. Prove that 
.Attachments:
