Finding the minimum value of $a^2+b^2+c^2$ 
Let $a$, $b$ and $c$ be $3$ real numbers satisfying $2 \leq ab+bc+ca$. Find the minimum value of $a^2+b^2+c^2$. 

I've been trying to solve this, but I don't really know how to approach this. I thought of $(a+b+c)^2 = a^2+b^2+c^2 + 2(ab+bc+ca)$, but that gives me  $a+b+c$, which is unknown. How can I solve this?

Scalar product:
Let $\vec A : = (a,b,c)$, $\vec B: = (b,c,a)$.
$|\vec A \cdot \vec B| \le |A| |B| $.
$\Rightarrow$  :
$2 \le ab +bc + ca \le a^2 +b^2 + c^2$.
Equality: 
$a=b=c = \sqrt{\frac{2}{3}}$.
