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Math Help - How to find the radius of the green circle...Please help

  1. #1
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    How to find the radius of the green circle...Please help

    Please help in assisting me on how to complete this problem. Thanks much!!!
    Attached Thumbnails Attached Thumbnails How to find the radius of the green circle...Please help-screenshot-2014-06-20-15.59.16.png  
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  2. #2
    Senior Member Educated's Avatar
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    Re: How to find the radius of the green circle...Please help

    There may be an easier way, but I'd just try to find an equation for the circle, on the cartesian plane.

    The green circle I presume has radius 20, so the equation is

     x^2 + y^2 = 20^2

    The red circle has unknown radius and unknown shift, so the equation is:

     (x - h)^2 + (y - h)^2 = c^2

    We know 3 points on the red circle, based on your drawing:
    (0,20)
    (20,0)
    (-18 \sin \frac{ \pi}{4}, 18 \sin \frac{ \pi}{4})

    Now with this information you can solve for the equation of the red circle and hence the radius.
    Last edited by Educated; June 21st 2014 at 01:09 AM.
    Thanks from topsquark
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  3. #3
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    Re: How to find the radius of the green circle...Please help

    distance between centers = x

    radius of red circle = 18 + x

    there is a triangle with sides 20, x and 18 + x and an angle 135 degrees
    Thanks from ebaines and topsquark
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  4. #4
    Member jonah's Avatar
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    Re: How to find the radius of the green circle...Please help

    You could torture yourself working this all out
    or you could just use WolframAlpha
    circle through (-20, 0), (-9*sqrt (2), 9*sqrt (2)), (0, 20) - Wolfram|Alpha Results
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  5. #5
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    Re: How to find the radius of the green circle...Please help

    Idea's solution (post 3) requires only the solution of a linear equation; not much torture here.

    Thanks from topsquark and jonah
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  6. #6
    Member jonah's Avatar
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    Re: How to find the radius of the green circle...Please help

    Quote Originally Posted by johng View Post
    Idea's solution (post 3) requires only the solution of a linear equation; not much torture here.
    Can't argue with that. Still torture though when I took a whack at it totally sober using
    (-20-h)^2-(0-k)^2=r^2
    (-9*2^.5-h)^2+(9*2^.5-k)^2=r^2
    (0-h)^2-(20-k)^2=r^2

    Moral: Never take on someone else's math troubles sober. You'll end up suffering needlessly.
    Last edited by jonah; June 24th 2014 at 12:41 AM.
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  7. #7
    Member jonah's Avatar
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    Re: How to find the radius of the green circle...Please help

    Quote Originally Posted by jonah View Post
    (-20-h)^2-(0-k)^2=r^2
    (-9*2^.5-h)^2+(9*2^.5-k)^2=r^2
    (0-h)^2-(20-k)^2=r^2
    Major screw up. Should be
    (-20-h)^2+(0-k)^2=r^2
    (-9*2^.5-h)^2+(9*2^.5-k)^2=r^2
    (0-h)^2+(20-k)^2=r^2
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