= Solution
Assume a central eclipse and nearly uniform projected <speed> during it. Let $r$ be the smaller <radius> and $R$ the larger. First-to-second contact requires travel $2r$, whereas the totality interval requires $2(R-r)$. With relative <speed> 200 km s$^{-1}$,
$$
\boxed{r=\frac{v(1.7\ \mathrm h)}2\simeq6.12\times10^5\ \mathrm{km},\qquad R=r+\frac{v(0.8\ \mathrm h)}2\simeq9.00\times10^5\ \mathrm{km}.}
$$
The <light curve> has ingress, flat minimum and egress lasting 1.7, 0.8 and 1.7 hours. At the four contacts the projected center separations are $R+r,R-r,R-r,R+r$. A noncentral chord would require an <impact parameter> and changes the inferred radii; the data alone do not fix that geometry exactly. For comparable masses in an ordinary coeval system, a component larger than its <main sequence> companion suggests expansion away from the <main sequence>, conventionally toward a subgiant/early giant track. That is a conditional evolutionary interpretation: neither <effective temperature> nor a bolometric flux is supplied, so a unique position on the <Hertzsprung-Russell diagram> cannot be inferred from these radii alone. Binary interactions and the assumed central chord also matter; these numbers do not establish an ordinary single-star evolutionary model.
\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/2016-eclipse-and-microwave-sky.png]
{title=Central-eclipse contact geometry and schematic microwave sky components}
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