be a triangle 
)
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, Mango247, Rounak_iitr
Let 
be a convex quadrilateral with these properties: 
and 
.
If
, prove that 
.
by Mahdi Etesami Fard
be a convex quadrilateral with these properties: 
and 
.If
, prove that 
.by Mahdi Etesami Fard
This post has been edited 1 time. Last edited by parmenides51, Feb 25, 2024, 4:26 PM
then 
and 
. So 
and 
.
is right-angled in 
and with one angle of 45 . Evaluate 
and also 
and find 
and 
in terms of 
comes out to be as 
??
then 
and 
