A) $ \frac2\sqrt33 \cdot \fracr^2\textArea = 1 $ → Area ratios: $ \frac2\sqrt3 s^26\sqrt3 r^2 = \fracs^23r^2 $, and since $ s = \sqrt3r $, this becomes $ \frac3r^23r^2 = 1 $? Corrección: Pentatexto A) $ \frac2\sqrt33 \cdot \fracr^2\textArea $ — but correct derivation: Area of hexagon = $ \frac3\sqrt32 s^2 $, inscribed circle radius $ r = \frac\sqrt32s \Rightarrow s = \frac2r\sqrt3 $. Then Area $ = \frac3\sqrt32 \cdot \frac4r^23 = 2\sqrt3 r^2 $. Circle area: $ \pi r^2 $. Ratio: $ \frac\pi r^22\sqrt3 r^2 = \frac\pi2\sqrt3 $. But question asks for "ratio of area of circle to hexagon" or vice? Question says: area of circle over area of hexagon → $ \frac\pi r^22\sqrt3 r^2 = \frac\pi2\sqrt3 $. But none match. Recheck options. Actually, $ s = \frac2r\sqrt3 $, so $ s^2 = \frac4r^23 $. Hexagon area: $ \frac3\sqrt32 \cdot \frac4r^23 = 2\sqrt3 r^2 $. So $ \frac\pi r^22\sqrt3 r^2 = \frac\pi2\sqrt3 $. Approx: $ \frac3.143.464 \approx 0.907 $. None of options match. Adjust: Perhaps question should have option: $ \frac\pi2\sqrt3 $, but since not, revise model. Instead—correct, more accurate: After calculation, the ratio is $ \frac\pi2\sqrt3 $, but among given: - Veritas Home Health