be positive real numbers such that : 
. Prove that : 
.
and 
to 
to 
and 
as the reflections of 
be the circumcircle of 
.
with 
with 
is the circumcenter of 
can be inscribed within a circle.
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 
.
?
Y by
Circle 
inscribed in quadrilateral 
touches sides 
and 
at points 
and 
, respectively. Diagonal 
intersects the circle at the points 
and 
(the point lies on segment 
). Prove that lines 
, 
and 
intersect at one point.
Kozepiskolai Matematikai Lapok, 2013:09
inscribed in quadrilateral 
touches sides 
and 
at points 
and 
, respectively. Diagonal 
intersects the circle at the points 
and 
(the point lies on segment 
). Prove that lines 
, 
and 
intersect at one point.Kozepiskolai Matematikai Lapok, 2013:09
This post has been edited 1 time. Last edited by parmenides51, May 9, 2022, 6:14 PM
