.
min
be a triangle. Let 
be the feet of the altitudes from 
respectively. Let 
be the projections of 
.
.
be real numbers such that ![\[ \frac{1}{x^2-1} + \frac{1}{y^2-1} + \frac{1}{z^2-1} = 1. \]](http://latex.artofproblemsolving.com/8/f/5/8f5d49c9b44e3db3cd85fea7b6521e1dc02d4269.png)
Prove that ![\[ \frac{1}{x+1} + \frac{1}{y+1} + \frac{1}{z+1} \le 1. \]](http://latex.artofproblemsolving.com/c/0/4/c0438d6eba686d0a11fd4decb4afa9a14aa50bac.png)
are non-negative integers.
Y by
Let 
be a convex quadrilateral with perpendicular diagonals intersecting at 
. Prove that the reflections of across 
, BC, CD, DA$ are concyclic.
be a convex quadrilateral with perpendicular diagonals intersecting at 
. Prove that the reflections of across 
, BC, CD, DA$ are concyclic.
