be an acute-angled triangle with 
.
be the orthocenter of triangle 
,
be the midpoint of the side 
.
be a point on the side 
and 
a point on the side 
such that 
and the points 
is perpendicular to the common chord of the circumscribed circles of triangle 
.
. Prove that
and 
. Prove that
Thank lbh_qys.
and 
Prove that 
.
![\[
a_7 \cdot 3^7 + a_6 \cdot 3^6 + a_5 \cdot 3^5 + a_4 \cdot 3^4 + a_3 \cdot 3^3 + a_2 \cdot 3^2 + a_1 \cdot 3^1 + a_0 \cdot 3^0
\]](http://latex.artofproblemsolving.com/0/c/e/0ce2c259010b678238f11d35fc1328ea76f945f6.png)
where 
for 
?
and 
are in the coordinate plane such that 
.
denote the locus of all points 
in the coordinate plane satisfying 
,
and 
are on 
and 
.
can be expressed in the form 
,
and 
are relatively prime positive integers. Find 
.
sides and 
sides, respectively. The total number of sides is 33, and the total number of diagonals is 243. What are the values of 
but I am looking for the exact value. Does anyone know how to solve this problem?
knights and 
knight was already seated at the table so we don't have to take into account of the rotations if they were seated alternately. Though my solution does take into account of the different rotations of the knights and jokers.
Y by
Hi everyone
I actually didn't know where to ask this question, so i'm sorry for asking here
Do you know a good resource for learning complex numbers? something like book..
What about a good resource for learning polynomial Interpolation?
Thanks
I actually didn't know where to ask this question, so i'm sorry for asking here
Do you know a good resource for learning complex numbers? something like book..
What about a good resource for learning polynomial Interpolation?
Thanks
