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A circle is inscribed in a regular hexagon with side length 20.  What is the radius of the circle?

 Jun 9, 2020
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Draw the regular hexagon and the inscribed circle.

Draw a triangle from the center of the circle, along a radius to a point of tangency of the circle and the 

hexagon, and along the tangent to a corner.

This triangle is a 30o-60o-90o triangle with the length of the side from the point of tangency to the

corner = 10.

This will make the radius = 10·sqrt(3).

 Jun 9, 2020

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