be a function such that for every regular 
-
we have 
.
for all reals 
.
)
are the altitudes of the triangle. The bisector of 
intersects 
at 
.
be a point such that 
and 
.
passes through the midpoint of 
& 
.
with 
and at most one of them being zero, show that![\[\frac{1}{\max(a^2,b)}+\frac{1}{\max(b^2,c)}+\frac{1}{\max(c^2,a)}\geq\frac{27}{4}\]](http://latex.artofproblemsolving.com/9/e/1/9e14a9ef2d1a0a98006bcf716fa33c3d9ea29bd5.png)
Y by Adventure10
In the isosceles triangle 
(
), let 
be a line parallel to 
through 
. Let 
be an arbitrary point on . Let 
be the feet of perpendiculars through to 
respectively. Suppose that 
are the images of on . Prove that 
Proposed by Morteza Saghafian
(
), let 
be a line parallel to 
through 
. Let 
be an arbitrary point on . Let 
be the feet of perpendiculars through to 
respectively. Suppose that 
are the images of on . Prove that 
Proposed by Morteza Saghafian
This post has been edited 1 time. Last edited by bgn, Sep 15, 2017, 10:42 AM
be the reflection of 
to 
be the perpendicular from 
.
is the projection of 
.
.
.
is the projection of 
onto 
.
be the reflection of 
So,
