If a circle of constant radius '$$r$$' passes through the origin and meets the coordinate axes at points $$A$$ and $$B$$ respectively, then the locus of the centroid of triangle $$O A B$$, '$$O$$' being the origin, is

The image of the centre of the circle $$x^2+y^2=a^2$$ with respect to the mirror $$x+y=1$$ is

The radius of the circle $$(x \cos \theta+y \sin \theta-a)^2+(x \sin \theta-y \cos \theta-b)^2=k^2$$ is