Formulas to look into for stellar radius: Small angle formula (if the star can be resolved with some angular size, and if you know the distance to it by trig parallax or distance modulus because you have spectra or it is a standard candle, then you can find the physical size of the object), binary star relationships (if you have a really funky planet system around a binary star...that may be tricky unless the problem is simplified), the Stefan-Boltzmann Law (you can find luminosity class and temperature from its spectra, and then with that you can directly solve for radius). Note that you could want to use all three methods to find errors between them, and that would be real science because what would cause the errors! These are all essentials to the event, if they're not mentioned in the rules (I think they are, but I don't feel like getting them up right now), then I believe at least the astro webinar and other resources mention this.
What is really appreciated in questions more than just "making stuff up" (not to anyone specific) is actually making it appropriate to how a real astronomer would find out and correct the data! To even start finding out about planets, you certainly need to know a thing or two about stars, among many other complexities. I could imagine MANY errors related to exoplanetary science in some way relates to errors in our understanding of stellar astro. Stars shine their light onto planets, have variability that can affect our interpretation of light curves, and are related even to transmission spectra as I recall. Why the year still involves stellar evolution and basic stellar math
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. The test was around half about DSOs and facts, while the other half was mostly calculation oriented. Oh well, I hope we can do it next year!
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