[/quote]
,
such that 
,
,
with center 
and radius 
.
the midpoint of side 
intersects the circle 
.
be a point on the circle 
and 
.
.
.
and from 
to 
and 
as the reflections of 
and 
be the circumcircle of 
.
the second intersection of line 
with 
the intersection of ray 
with 
is the circumcenter of 
can be inscribed within a circle.
![\[\sqrt{a+h_B}+\sqrt{b+h_C}+\sqrt{c+h_A}=\sqrt{a+h_C}+\sqrt{b+h_A}+\sqrt{c+h_B}\]](http://latex.artofproblemsolving.com/5/d/6/5d6881be29327bcdc3e7bd76c221968578c7f50b.png)
is isosceles.
be all the divisors of 
are all divisors for some 
(
)
be a sequence of positive real numbers that satisfies 
and 
for every natural number 
for every natural number 
and 
.
?
be positive real numbers such that : 
. Prove that : 
be the set of positive integers. Find all functions 
such that![\[ m^2 + f(n) \mid mf(m) +n \]](http://latex.artofproblemsolving.com/2/f/4/2f409d1de993f1af8fd839bb8e9f87a57e1b8608.png)
and 
(ans- 
)
satisfying 
Prove that 
When does equality hold?
Y by Adventure10, Mango247
A regular 
-gon is inscribed in a circle radius 
. Let 
be the set of all arcs 
, where 
are distinct vertices of the -gon. 
elements 
of are chosen at random (so two or more of the 
can be the same). Show that the expected length of 
is independent of .
-gon is inscribed in a circle radius 
. Let 
be the set of all arcs 
, where 
are distinct vertices of the -gon. 
elements 
of are chosen at random (so two or more of the 
can be the same). Show that the expected length of 
is independent of .This post has been edited 1 time. Last edited by parmenides51, Jan 20, 2020, 4:48 PM
