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Math Help - I need help with circumscriptive geometry!

  1. #1
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    Exclamation 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
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  2. #2
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    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
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  3. #3
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    circumscriptive geometry

    Quote Originally Posted by mackenzieee View Post
    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
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