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
In right 
, 
and 
are on legs 
and 
, respectively, such that 
. Through the point of intersection, 
, of 
and 
, a line is drawn also passing through 
and meeting the hypotenuse 
at 
. The extension of 
meets line at 
. Suppose 
, and 
. Then, if the length of 
is 
, find .
, 
and 
are on legs 
and 
, respectively, such that 
. Through the point of intersection, 
, of 
and 
, a line is drawn also passing through 
and meeting the hypotenuse 
at 
. The extension of 
meets line at 
. Suppose 
, and 
. Then, if the length of 
is 
, find .
