Circumscriptive Geometry Question

[Jet_Master]

As you can read from the title, this is a "Circumscriptive Geometry Question"...
read on...

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 simplified and exact form, the ratio of the area of the smallest circle to that of the largest.

Note: within a regular polygon, the distance from its center to any given vertex is called its radius. The length of a perpendicular from its center to any given side is called its apothem.

I got this question from a website, Here is the URL

if you are posting a solution, please also post the steps to the full solution please...

(by the way, i already got the answer to this and i konw what is the correct answer)

[Jet_Master]

i think that is about the correct answer...
but it say's "ratio of the area of the smallest circle to the biggest one... so it would be the other way (ie. 3:16), and simplified it would be 1:5.333....

i would like to see the steps, if its okay with you..

[Captain Penguin]

Could this be an odd-numbered problem in a textbook?

[Jet_Master]

oh there it is... i had been looking for this thread for sometime now and could not find it... (wtf's wrong with me!!!)

anyway... i think those steps work... thats pretty good, except i didnt get the how AC is the radius of the extertior circle... there is a hexagon, another circle and a triangle to go before the last circle...
anyway, who cares? you got the answer and showed the steps, thats all that matters..