Thread: I need help with circumscriptive geometry!

Hi everyone!

I need help with this confusing math problem!

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.

I understand how I am supposed to draw it, but how do I get numbers and eventually a ratio?

Thanks for your help

Mackenzie

I would draw as follows.

1) line A from the circle centre (cc) to the mid point of one side of the hexagon.
2) line B from cc to an end of the same line.
This gives a right angled triangle angle between A and B is 30 deg.
3)On the end of line B have the centre of one side of the equilateral triangle.
continue as previous steps

Originally Posted by mackenzieee

Hi everyone!

I need help with this confusing math problem!

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.

I understand how I am supposed to draw it, but how do I get numbers and eventually a ratio?

Thanks for your help

Mackenzie

Did you draw it? If not I suggest you do making it large enough to clearly see all lines and angles.You will see that all calculations involve 30-60-90 triangles. Work up from 1 to the radius of the largest circle.The area ratio is the square of that circle to1.Use the 2-1-rad 3 relationship