This apparent contradiction between the chlorine ion and the sodium ion is; due to electrostatic attraction between the nucleus and the electrons.
As we know, there's a periodic trend for atomic radii in the periodic table; the trend is as follows;
Elements get larger down the group and this explains the trend down a group.
Consequently, when Chlorine forms an ion by gaining an electron, the electrostatic attraction between its nucleus and electrons increases and the the atomic radius decreases.
On the other hand, when sodium forms an ion by losing an electron, the electrostatic attraction between its nucleus and electrons decreases and the the atomic radius increases.
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