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![\[
\sqrt{x-3}+\sqrt{6-x} \leq p
\]](http://latex.artofproblemsolving.com/3/2/b/32b8bf5c8aa4d7561933e38ee0e2a0480e1a2f07.png)
In which 
, hence find the largest value of 
.
where 
is a monic polynomial of degree 
satisfying 
where is a polynomial of smallest degree possible satisfying 
and 
, if polynomial satisfies 
where is a polynomial of smallest degree satisfying 
and 
if polynomial satisfies 
is a polynomial of degree 
such that 
Evaluate 
be the feet of the perpendiculars from the vertices 
of triangle 
. Let 
be the circumcenter . Prove that ![\[ OA \perp FE .\]](http://latex.artofproblemsolving.com/a/9/d/a9db29e528d86ad6b58f68ccfca298245f167894.png)
EBand
DFand let
AGbe perpendicular to
BCthrough
A. Then, since
\angle HDA=\angle AFH=90°, the quadrilateral
AEHFis cyclic. Thus, we have
\angle AFE=\angle AHE=\angle GHB=90°-\angle EBC=\angle BCA. Finally, since
\angle HAE=90°-\frac{1}{2}\angle BHA=90°-\angle BCA, the conclusion follows.
AEFand
ABCare similiar.
to meet the circumcircle in 
.
is inscriptible and finally show that
.
