and 
Prove that
Let 
and 
Prove that
prove that![\[ \frac{a^2}{b^2} + \frac{b^2}{c^2} + \frac{c^2}{d^2} + \frac{d^2}{a^2}\geq\frac{a}{d} + \frac{b}{a} + \frac{c}{b} + \frac{d}{c}\]](http://latex.artofproblemsolving.com/0/0/4/004e7f148bbb0c797688f5195aa4002dbc316470.png)
If you know same tasks, link them please
be the Fermat point of a 
.
,
,
are concurrent and the point of concurrence is 
,
(
well). i want to study so if you guys have some easy or normal problems please send me
Y by
Points 
and 
are chosen inside an acute-angled triangle 
with altitude 
so that 
, and 
. Point 
is chosen on the ray 
so that lies on segment 
and 
, and point 
is chosen on the ray 
so that lies on segment 
and 
. Prove that 
.
Proposed by Mykhailo Shtandenko
and 
are chosen inside an acute-angled triangle 
with altitude 
so that 
, and 
. Point 
is chosen on the ray 
so that lies on segment 
and 
, and point 
is chosen on the ray 
so that lies on segment 
and 
. Prove that 
.Proposed by Mykhailo Shtandenko
.
which is the same as if 
and 
were swapped, so 
