The  distance of the origin from the circumcenter of a triangle with vertices $(3,6,6),(6,3,6),(6,6,3)$is $\lambda \sqrt{3}$ then $\lambda =$

Let $A(3,6,6),B(6,3,6),C(6,6,3)$
$\Rightarrow AB=BC=CA=\sqrt{3^2+3^2}=3\sqrt{2}$
The triangle is equilateral. The circumcentre is the centroid,
$\left(\frac{3+6+6}{3},\frac{6+3+6}{3},\frac{6+6+3}{3}\right)=(5,5,5)$
Its distance from the origin is
$\sqrt{5^2+5^2+5^2}=5\sqrt{3}$.