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 a coordinate system, a circle with radius 
and center is on the y-axis placed inside the parabola with equation 
, so that it just touches the parabola in two points. Determine the coordinate set for the center of the circle.
and center is on the y-axis placed inside the parabola with equation 
, so that it just touches the parabola in two points. Determine the coordinate set for the center of the circle.
.
.
.
and 
again by symmetry.
into our equation of the circle yields 
.
,
.
.
.
