Circumscriptive Geometry Help!!

[mackenzieee]

About a unit circle, a regular hexagon is circumscribed, about which another circle is circumscribed, about which an equilateral triangle is circumscribed, about which a third circle is circumscribed. Find, in simplest and exact form, the ratio of the area of the smallest circle to that of the largest.

What do I do!?!?? Thank you so much guys!

 

[Denis]

What do I do!?!??

Do your best :wink:

Did you draw a diagram?

 

[garf]

I obtained that the reason is; 2.31

 

[Denis]

I get 3:16

Hexagon sides = 2 / SQRT(3) = radius of circle circumscribing hexagon

a = side equilateral triangle
aSQRT(3) / 6 = 2 / SQRT(3)
a = 4

radius circle circumscribing triangle = aSQRT(3) / 3 = 4 / SQRT(3)

area inner circle = pi 1^2 = pi
area large circle = pi [4 / SQRT(3)]^2

pi / pi [4 / SQRT(3)]^2 = 3/16