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Math Help - radius of a circle puzzle

  1. #1
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    radius of a circle puzzle

    I need help with this problem..even asked several friends but no1 knows what to do :[

    heres a little picture

    so the answer is: 6 - (square- root-10) .. but i have no clue how to even get that.
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  2. #2
    MHF Contributor red_dog's Avatar
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    We have OA=R, \ OB=R-1, \ AB=5-R
    Apply Pitagora in AOB:
    R^2=(R-1)^2+(5-R)^2\Rightarrow R^2-12R+26=0
    Solving for R, the good solution is R=6-\sqrt{10}
    Attached Thumbnails Attached Thumbnails radius of a circle puzzle-fig.jpg  
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  3. #3
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    oh wow, thank you very much
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