The side of a regular hexagon is 2 cm. Then, what is the ratio of the radius of the circumscribed circle to the radius of the inscribed circle?

# The side of a regular hexagon is 2 cm. Then, what is the ratio of the radius of the circumscribed circle to the radius of the inscribed circle?

1. A

2. B

3. C

4. D

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### Solution:

Let the diagram of the given situation be,
From the above figure, EO is the diameter of the circumscribed circle.
In triangle EMF, we have

O is the center of the hexagon. Then,

Then, the radius of the circumscribed circle is,

From the figure, we can say that PO is the radius of the inscribed circle. Since  , then

The ratio of the radius of the circumcircle and incircle is given by  .
Hence, the correct option is 1.

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