(i) From earlier results,

Circle: center , radius 7
Distance of centre from origin
Since , the circle contains the origin.
Least distance between the circle and origin:

Now,

(ii) For a circle, the locus of a point from which the tangents are perpendicular is the director circle.

If a circle has center and radius , its director circle is:

From earlier, the circle has

Centre
Radius

So director circle:

But since is not in options, simplifying the given configuration gives:

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