A circle having center $(0,k)$, with $k>6$,is tangent to the lines $y=x$, $y=-x$ and $y=6$. What is the radius of this circle? $\mathrm{(A)}\ 6\sqrt{2}-6 \qquad$ $ \mathrm{(B)}\ 6 \qquad$ $ \mathrm{(C)}\ 6\sqrt{2} \qquad$ $ \mathrm{(D)}\ 12 \qquad$ $ \mathrm{(E)}\ 6+6\sqrt{2}$