= Solution
TODO: the source light curve, its numerical contact phases and the meanings of the four plotted time labels are absent, so unique numerical stellar radii cannot be recovered. The <central eclipse contact-radius relations> explain what the missing measurements would determine.
If $t_1,\ldots,t_4$ denote the usual first through fourth contacts of a central eclipse, define $T_{14}=t_4-t_1$ and $T_{23}=t_3-t_2$, and let $R_L\ge R_S$ be the two radii. For a circular edge-on orbit,
$$
R_L+R_S=a\sin\frac{\pi T_{14}}P,\qquad
R_L-R_S=a\sin\frac{\pi T_{23}}P.
$$
Taking half their sum and difference gives the radii. For short eclipses the familiar approximation is $R_L\simeq v_{\rm rel}(T_{14}+T_{23})/4$ and $R_S\simeq v_{\rm rel}(T_{14}-T_{23})/4$, with $v_{\rm rel}=2K$. At first and fourth contact the discs touch externally; at second and third the smaller disc is just internally tangent to the larger. Noncentral eclipses require the projected impact parameter as well.
\Image[/past-exam-of-the-short-options-paper-shared-by-prelims-and-parts-a-and-b-of-the-physics-course-of-the-university-of-oxford/2012-s2-central-eclipse-contacts.png]
{title=Conditional central-eclipse contact geometry; this schematic supplies no readings from the missing source light curve}
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