then prove \frac{1}{a+b}+\frac{1}{b+c}+\frac{1}{c+a}+\frac{1}{2}\cdot\frac{abc}{ab+bc+ca}\ge \frac{5}{3}.$$
and 
Prove that
Let 
Prove that
Let 
Prove that
Let 
Prove that
Y by
Let 
and 
be the circumcenter and incenter of 
respectively. If 
, points 
are midpoints of 
respectively and 
, then prove that the line 
and the bisector of 
are perpendicular .
and 
be the circumcenter and incenter of 
respectively. If 
, points 
are midpoints of 
respectively and 
, then prove that the line 
and the bisector of 
are perpendicular .
intersect the circumcircle of 
in 
=
=
:
+
=
=
=
=
& 
=
=
=
=
