Find the length of the perimeter of a regular decagon which surrounds a circle of radius 12cm.

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60 cm

66 cm

72 cm

78 cm

answer is D.

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Detailed Solution

Given that the decagon surrounds the circle.
radius of the in-circle, r = 12 cm
Side of the regular decagon is n=10
Let, length of the regular decagon be l.

l = 2 rtan \frac{180^{\circ}}{n} = 2 \times 12 \times \tan \frac{180^{\circ}}{10} = 24 \times \tan 18^{\circ} = 24 \times 0.32492 = 7.79 cm

∴ Perimeter =10l

\approx

78 cm

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