Which of the following is a direct consequence of the lanthanoid...

The lanthanoid contraction refers to the steady decrease in atomic and ionic radii across the lanthanoid series due to the poor shielding effect of the $4f$ electrons.

A direct consequence of this contraction is that the atomic radii of the elements of the third transition series ($5d$) become almost identical to those of the corresponding elements of the second transition series ($4d$). For example, the atomic radii of $Zr$ ($160$ pm)$and Hf$ ($159$ pm) are nearly the same.

Regarding the other options:
As the size of the $Ln^{3+}$ ion decreases from $La^{3+}$ to $Lu^{3+}$, its polarizing power increases. According to Fajans' rules, this increases the covalent character of the $Ln-OH$ bond, which in turn decreases the basic character of the hydroxides from $La(OH)_3$ to $Lu(OH)_3$.
The separation of lanthanoids is actually very difficult because their similar sizes lead to almost identical chemical properties.

Answer: The atomic radii of the elements of the second transition series (4d) are almost identical to those of the corresponding elements of the third transition series (5d).