Do you need to know the distance to a star to work out the radius of any planets it has?
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No. . . but,
How you will estimate the radius of an exoplanet depends on how it was detected. In the simplest case of a transiting exoplanet, you can look at the light curve and see how much the brightness of the star drops as the planet passes in front of the star. That can tell you the relative size of the planet compared to the star. If you can get an estimate of the radius of the star (from a model of stars of a given type) you can estimate the radius of the planet.
There are problems in this method if the planet doesn't pass directly in front of the star: a grazing transit. Or if the star is variable, or has star-spots, or if the data is noisy. Your estimate may have quite wide error margins.
The RGO has a guide for students on how this can be done
If you have detected the planet by the radial velocity method (detecting motions of the star as it is pulled by the gravity of a planet) then estimating the radius is harder. A small dense planet will cause exactly the same wobble to the star as a large fluffy planet. You may get a good estimate of planetary mass from this kind of detection, and use that, combined with a predicted temperature of the planet, to determine if it is likely to be an ice, gas or rocky planet, and with that assumption make an estimate of the radius.
Thus the radial velocity method gives information about mass, and the transit method gives information about radius.
If you have directly imaged the planet, then using an estimate for the albedo and an estimate for the distance of the stellar system, you can estimate the radius of the planet from its apparent brightness.
If the planet has been detected by micro-lensing, then there is probably no way to get a useful estimate of radius, except with the most generous error margins.
