functions - Solution to functional equation and Cauchy

I want to show that the only continuos solutions to the functional equation
$g(x)+g(y)=g(\sqrt{x^2+y^2})$

is $g(x)=cx^2$ where c is a constant i.e. c=g(1).

I think that I maybe could rewrite the equation, such that I could use the solution to Cauchy's functional equation i.e.

$f(x+y)=f(x)+f(y)$
with solutions $cf(x)$, but i can't see how. Can anyone give med a hint?