Hexagon around a circle that has a diameter of 104

Question

What's the length of each side ??

Answer 1

The radius of the circle, 52, is the apothem of the hexagon

It is the long leg of a 30-60-90 triangle

What is the length of the hypotenuse ?

 

Answer 2

First, let's notice that the Radius = 0.5D (diameter) or 52 and the half of the length of the circumscribed Hexagon side S relates to the radius as per the following equation:

 

S/2 = R*tan(30^o)

 

therefore

 

S = 2R * (1/√3) =104/√3 ≅ 60