Suppose a circle of radius r is inscribed in a hexagon. What is the perimeter of the hexagon? Thanks!

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Answer 1 · 2018-02-13T22:36:14

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Let length of each side of the regular hexagon circumscribing the circle of radius $r$ be $a$ .

Then obviously
$(a/2)/r=cot60^@$
$=>a=2rcot60^@=2r*1/sqrt3$ .
So perimeter of the hexagon will be $=6a=12/sqrt3r=4sqrt3r$

Suppose a circle of radius r is inscribed in a hexagon. What is the *perimeter* of the hexagon? Thanks!