[/quote]
,
such that 
,
,
with center 
.
the midpoint of side 
intersects the circle 
be a point on the circle 
and 
.
.
.
and from 
and 
as the reflections of 
and 
be the circumcircle of 
.
the second intersection of line 
with 
the intersection of ray 
with 
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
Circles 
and 
intersect at points 
and 
, and the circle with center at point 
covers circles and , touching them at points 
and 
respectively. It turned out, that the points 
and lie on the same straight line. Find the angle 
.
and 
intersect at points 
and 
, and the circle with center at point 
covers circles and , touching them at points 
and 
respectively. It turned out, that the points 
and lie on the same straight line. Find the angle 
.This post has been edited 2 times. Last edited by parmenides51, May 28, 2022, 5:31 AM
Reason: source
Reason: source
and 
are centers of 
and 
lies on same lines. So 
and same way 
so 
is paralelogram.
is point of intersection of 
and 
.
so 
is midline and so 
.
so 
