= Solution
Assume spherical <stars>, central eclipses, uniform disc <surface brightness>, and negligible third light. Let $s$ denote the smaller <star> and $\ell$ the larger one, with $r=R_s/R_\ell\leq1$ and $\ell_s=L_s/L_\ell$. Normalize the out-of-eclipse <flux> to one, and denote the deep and shallow fractional losses by $D$ and $d$. The graph gives approximately $F_{\rm out}\simeq0.98$, $F_{\rm deep}\simeq0.57$, $F_{\rm shallow}\simeq0.90$, so $D\simeq0.42$, $d\simeq0.08$; the last digits are graphical estimates.
At total occultation of the smaller <star>, the lost <flux> is $L_s/(L_s+L_\ell)$. At its central transit across the larger <star>, the lost <flux> is $r^2L_\ell/(L_s+L_\ell)$. There are two identifications:
* \b[Smaller star hidden at the deep eclipse.] Then $D=\ell_s/(1+\ell_s)$ and $d=r^2/(1+\ell_s)$, giving $\ell_s=D/(1-D)$ and $r=\sqrt{d/(1-D)}$. Thus $\boxed{R_s/R_\ell\simeq0.37,\quad L_s/L_\ell\simeq0.72}$. The smaller <star> has the higher <surface brightness>; the deep eclipse hides it and the shallow eclipse is its transit.
* \b[Smaller star hidden at the shallow eclipse.] Then $d=\ell_s/(1+\ell_s)$ and $D=r^2/(1+\ell_s)$, giving $\ell_s=d/(1-d)$ and $r=\sqrt{D/(1-d)}$. Thus $\boxed{R_s/R_\ell\simeq0.67,\quad L_s/L_\ell\simeq0.089}$. The smaller <star> has the lower <surface brightness>; the deep eclipse is its transit across the hotter, larger <star>.
These are ratios of <luminosities> in the observed band. Treating them as bolometric <luminosities> requires similar band corrections or an explicitly bolometric <light curve>. <Limb darkening> and finite exposure times limit the precision of these elementary estimates.
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