= Solution
<Exoplanet transit photometry> discovers a giant planet through a periodic flux decrement and measures $R_p/R_\star\simeq\sqrt{\delta}$. Stellar-radius estimates turn this into a planetary radius. The <radial-velocity method> discovers the stellar orbital reflex motion and constrains $M_p\sin i$. Follow-up <exoplanet transit photometry> is required to measure a geometric radius when such a planet also transits; a radial-velocity detection alone gives no direct size. Alternatively, <exoplanet direct imaging> finds young luminous giants, whose sizes are inferred less directly from luminosity, <temperature>, distance, and a <planetary mass-radius relation> or atmosphere model.
The two broad explanations for <hot-Jupiter radius inflation> are retention of primordial heat and addition of new interior power.
<Delayed cooling of an inflated giant planet> can arise from enhanced atmospheric <opacity>, which slows radiative escape; an irradiation-maintained radiative blanket, which insulates the convective interior; or compositional stratification and inefficient <layered convection>, which inhibit the outward transport of heat. These alter the rate of <Kelvin-Helmholtz contraction>.
<Heating of an inflated giant planet> can arise from <tidal heating> maintained by eccentricity or obliquity; <Joule heating> of currents driven by atmospheric winds through a <magnetic field>; or downward transport and dissipation of atmospheric mechanical energy generated by irradiation. To affect radius, the energy must be deposited at a depth and rate that changes the interior cooling balance. Simply absorbing starlight high in the atmosphere does not automatically supply deep heating. These are proposed mechanisms with different efficiencies, not six universally established contributions in every inflated planet.
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