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Math Help - Find the radius

  1. #1
    A riddle wrapped in an enigma
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    Find the radius

    The rectangle in the corner is 6 units by 12 units. Find the radius of the circle.
    Attached Thumbnails Attached Thumbnails Find the radius-circle.png  
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  2. #2
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    Quote Originally Posted by masters View Post
    The rectangle in the corner is 6 units by 12 units. Find the radius of the circle.
    R = 30, No?
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  3. #3
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    Quote Originally Posted by Danny View Post
    R = 30, No?

    I think your answer is correct

     (R-6)^2 + (R-12)^2 = R^2

     R^2 - 36R + 180 = 0

     (R-30)(R-6) = 0

    but  R cannot be 6 so the answer is 30
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by masters View Post
    The rectangle in the corner is 6 units by 12 units. Find the radius of the circle.
    Quote Originally Posted by Danny View Post
    R = 30, No?
    Quote Originally Posted by simplependulum View Post
    I think your answer is correct

     (R-6)^2 + (R-12)^2 = R^2

     R^2 - 36R + 180 = 0

     (R-30)(R-6) = 0

    but  R cannot be 6 so the answer is 30
    Very good, guys! I didn't want to stress your brains too much, so this one was not a really big challenge. I'll spice it up a little more in the future.
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    "If radius = 30 and rectangle is w by 2w, find w"
    would have been "fun"
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    Quote Originally Posted by Wilmer View Post
    "If radius = 30 and rectangle is w by 2w, find w"
    would have been "fun"

    In general

     (R - \omega)^2 + (R - 2\omega)^2 = R^2

     R^2 - 2R( \omega + 2\omega ) + {\omega}^2( 1 + 2^2 ) = 0

     R^2 - 6R(\omega) + 5{\omega}^2  = 0

     ( R - 5 \omega )(R - \omega) = 0

    Therefore , the relationship between  R and  \omega is

     R = 5\omega

    or their ratio is 5
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