Can a black hole have a finite perimeter but an infinite radius/diameter?

Recently, I attended a talk at UNC Chapel Hill by Kip Thorne and I recall that he mentioned that black holes can have a finite perimeter but an infinite radius/diameter (since spacetime is curved with the instance of a black hole, general euclidian geometry isn't obeyed) Is this true, or am i misinterpreting/misremembering what he said?

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At any point outside a black hole, there is a pretty natural frame of reference to prefer, which is the frame of an observer who is at rest with respect to the black hole, at that point. After all, if I was going to measure some ordinary object like a tree, I would naturally prefer to measure it in the frame where it was at rest. This means that we can define the circumference $$C$$ of any circle centered on the black hole, as long as the circle lies outside the black hole. This also works in the limit as shrink the circle down as far as the event horizon.
For these circles, it's also conventional to define a radius $$r=C/2\pi$$. However, this $$r$$ is really just an arbitrary coordinate, not a distance that can be measured from the center. The reason is that once we go inside the black hole, it's no longer possible to have observers at rest relative to the black hole. So this "radius" isn't really a radius in the Euclidean sense. It's known as the Schwarzschild $$r$$ coordinate, and its value when the circle is shrunk down to the horizon is called the Schwarzschild radius $$r_s$$.