Three circles with unit radius touch each other and each of them touches a bigger circle externa...

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Three circles with unit radius touch each other and each of them touches a bigger circle externally. Find the area of the bigger circle that touches all three circles.
a. \( \left(\frac{7+4 \sqrt{3}}{3}\right) \pi \)
b. \( \frac{\pi}{3}(\sqrt{3}+2)^{2} \)
-c. \( \left(\frac{2+2 \sqrt{3}}{5}\right) \pi \)
d. None of these
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