[/quote]
,
be four distinct points in the plane.
and 
are distinct and parallel, then
is equal to the oriented angle DCB.
lies on the segment 
,
plus the oriented angle 
e
.
equals 0°, then
a
and 
be positive real numbers satisfying 
and 
Prove that![\[\frac{a}{(b+c-a)^2} + \frac{b}{(c+a-b)^2} + \frac{c}{(a+b-c)^2} \geq \frac{3}{(abc)^2}.\]](http://latex.artofproblemsolving.com/0/a/b/0ab4b4e6c28a1ae67788525642661dbcd04d0bd8.png)
and in 
steps and has to reach 
is valid but 
is not valid.
,
lie on a line in this order and satisfy 
.
and 
be the midpoints of 
and 
,
is acute, and let 
be its orthocentre. Points 
and 
lie on lines 
and 
,
and 
and 
and 
such for any 
.
satisfy,
Where 
}
be an integer. We are given a balance and 
weights of weight 
.
to satisfy that the equation 
has at least 1 roots 
of the equation![\[n^3=p^2-p-1\]](http://latex.artofproblemsolving.com/f/f/8/ff88093bb0aa93afcfdff3ae25149ec5fbacb61f.png)
is a prime number and 
?
Y by Adventure10
Let a triangle 
be given. On the 
side, the point 
is selected, on the 
side, the 
point is selected. Let 
, 
, 
be the midpoints of 
, 
, 
, respectively. On the ray 
, the point 
is chosen in such a way that 
, on the ray 
the point 
is chosen so that 
. Prove that 
be given. On the 
side, the point 
is selected, on the 
side, the 
point is selected. Let 
, 
, 
be the midpoints of 
, 
, 
, respectively. On the ray 
, the point 
is chosen in such a way that 
, on the ray 
the point 
is chosen so that 
. Prove that 
This post has been edited 2 times. Last edited by parmenides51, Jul 29, 2019, 7:30 PM
