The lanthanide contraction is responsible for the fact that

The steady decrease in the atomic and ionic radii of the trivalent lanthanides from $$La^{3+}$$ to $$Lu^{3+}$$ is called the lanthanide contraction.

This contraction is transmitted to the elements that come immediately after the lanthanide series, i.e. the $$5d$$ transition elements. As a result, the radii of the $$5d$$ elements become almost the same as those of their $$4d$$ congeners situated just above them in the periodic table.

Zirconium (Zr) is a $$4d$$ element (Group 4, period 5) while hafnium (Hf) is its $$5d$$ congener (Group 4, period 6). Because of the lanthanide contraction, the expected increase in radius from Zr to Hf is almost completely cancelled, so the two elements possess nearly identical atomic (and ionic) sizes.

Checking the given options:
A. Zr and Y (yttrium) are both $$4d$$ elements; their similar radius is not a consequence of lanthanide contraction.
B. Similar oxidation states of Zr and Nb arise from electronic configurations, not from lanthanide contraction.
C. Zr and Hf have about the same radius — this directly results from the lanthanide contraction ✔️
D. Zr and Zn belong to different groups; they neither have the same oxidation states nor is any relation caused by lanthanide contraction.

Therefore, the statement justified by lanthanide contraction is:

Option C which is: Zr and Hf have about the same radius