= Solution
As the star expands onto the <red giant branch>, a planet of fixed <radius> produces a shallower <exoplanet transit>, $\delta\propto R_\star^{-2}$. For a fixed circular <orbit> and an approximately central chord, duration grows approximately as $R_\star$, and transit probability also rises. At fixed <orbital inclination> the <impact parameter> in stellar-radius units decreases, further changing the chord. These statements neglect orbital evolution, stellar <mass loss>, tidal effects and eventual engulfment, all of which can matter for a very close planet.
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