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 Adventure10
In a triangle 
, the median 
(with 
on 
) and the angle bisector 
(with 
on 
) are perpedicular to each other. If 
and 
, find the integer nearest to the area of triangle .
, the median 
(with 
on 
) and the angle bisector 
(with 
on 
) are perpedicular to each other. If 
and 
, find the integer nearest to the area of triangle .
be the intersection of the lines 
.
so 
.
.
The answer is 
.
.
.
we have 
.![$[ABC]=AD*BX=7*9*(3/4) = 47.25$](http://latex.artofproblemsolving.com/1/7/0/170a5453ea46b317a7ab590a4fbb9d82a7e399e6.png)
is angle bisector and altitude, so 
is isosceles.
