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Math Help - Ratio of circumscribed triangle to inscribed triangle

  1. #1
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    Ratio of circumscribed triangle to inscribed triangle

    Equilateral triangle ABC has a circle inscribed in it. Inside the circle is inscribed another equilateral triangle, DEF. What is the ratio of AB to DE? (Answer from back of book: 4 to 1). I would expect the answer to be 2, but we don't know how to get the answer.

    I tried make a picture of what I mean (attached), but the letters came out wrong.

    Edit: Ignore the point labels in the figure. I need the ratio of one side of the big triangle to one side of the little triangle. Thanks.
    Attached Thumbnails Attached Thumbnails Ratio of circumscribed triangle to inscribed triangle-capture.png  
    Last edited by mathDad; March 20th 2013 at 01:31 PM.
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    Re: Ratio of circumscribed triangle to inscribed triangle

    Mathdad

    your figure is not correct. you put D at the barycenter of the triangle....
    Please give us more accurate information in order to help you.

    if you are searching for a ratio between the initial triangle ABC and the one inscribed then the ratio of their areas is 4:1
    Last edited by MINOANMAN; March 20th 2013 at 01:01 PM.
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    Re: Ratio of circumscribed triangle to inscribed triangle

    I know, but I am not skilled enough with Geogebra to change the letters. I said that in my first post, but thought I included enough information to make it clear what I wanted.

    I need the ratio of one side of the big triangle to one side of the small triangle. Thanks.
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    Re: Ratio of circumscribed triangle to inscribed triangle

    Quote Originally Posted by mathDad View Post
    I know, but I am not skilled enough with Geogebra to change the letters. I said that in my first post, but thought I included enough information to make it clear what I wanted.
    I need the ratio of one side of the big triangle to one side of the small triangle. Thanks.
    m(\overline{EH})=\frac{m(\overline{AB})}{2}.

    m(\overline{ED})=\frac{m(\overline{AE})}{3}

    m(\overline{AE})=\frac{\sqrt{3}m(\overline{AB})}{2  }
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  5. #5
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    Re: Ratio of circumscribed triangle to inscribed triangle

    Hi Dad,

    I hope the attached diagram answers your question:

    Ratio of circumscribed triangle to inscribed triangle-mhfgeometry15.png
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    Re: Ratio of circumscribed triangle to inscribed triangle

    Quote Originally Posted by johng View Post
    Hi Dad,
    I hope the attached diagram answers your question:
    Click image for larger version. 

Name:	MHFgeometry15.png 
Views:	7 
Size:	22.6 KB 
ID:	27619
    There is a problem with you diagram.
    It is not labeled the same as the one on the OP.
    Your O is his D.

    He did ask about \overline{ED}.
    Now, I will grant you that there seems to be a contradiction in his post.
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    Re: Ratio of circumscribed triangle to inscribed triangle

    Quote Originally Posted by johng View Post
    Hi Dad,

    I hope the attached diagram answers your question:
    Yes, very nice. Just the way I thought (the book must have a typo).
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  8. #8
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    Re: Ratio of circumscribed triangle to inscribed triangle

    Quote Originally Posted by Plato View Post
    There is a problem with you diagram.
    It is not labeled the same as the one on the OP.
    Your O is his D.

    He did ask about \overline{ED}.
    Now, I will grant you that there seems to be a contradiction in his post.
    Because the diagram in my OP is not correct. My bad.
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