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Math Help - Two Circle Problems

  1. #1
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    Two Circle Problems

    How do you do these two problems? (note: they are lifted from: a site called regentsprep.org).

    I feel like #6 is on the tip of my pencil. But I can't quite piece the info together. Circle 1 is x^2+y^2=16 and circle 2 is x^2+y^2=100. There must be some relationship (never mind that I reused x).

    But #7 seems like there isn't enough information, no matter how many new radii or inscribed angles I draw, I can't find any useful information.
    Attached Thumbnails Attached Thumbnails Two Circle Problems-six.png   Two Circle Problems-seven.png  
    Last edited by mathDad; March 22nd 2013 at 02:04 PM.
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  2. #2
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    Re: Two Circle Problems

    Quote Originally Posted by mathDad View Post
    How do you do these two problems? (note: they are lifted from: a site called regentsprep.org).



    I feel like #6 is on the tip of my pencil. But I can't quite piece the info together. Circle 1 is x^2+y^2=16 and circle 2 is x^2+y^2=100. There must be some relationship (never mind that I reused x).

    But #7 seems like there isn't enough information, no matter how many new radii or inscribed angles I draw, I can't find any useful information.
    to #6: Draw the cross-section of the sphere. Use Pythagorian theorem.

    to #7: Do you know what this sign means: \cong
    Attached Thumbnails Attached Thumbnails Two Circle Problems-schnittkreise.png  
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  3. #3
    MHF Contributor ebaines's Avatar
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    Re: Two Circle Problems

    #6 is easier than you think! You have a right angle triangle with one node from the center of the sphere , another at the center of the slice, and a third at the intersection of the slice and the edge of the spehere. You know the values for the radius of the sphere and the circle, so use Pythagoras to find x.

    Two Circle Problems-spheres.jpg

    #7 is so obvious you're just not seeing it. It would be similar to a problem like this: if x=y, and x=8, what is y?
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  4. #4
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    Re: Two Circle Problems

    Quote Originally Posted by earboth View Post
    to #6: Draw the cross-section of the sphere. Use Pythagorian theorem.

    to #7: Do you know what this sign means: \cong
    Congruent (it's like equals for objects). It means all the properties of one object match all the properties of the other object (except for position).
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  5. #5
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    Re: Two Circle Problems

    Quote Originally Posted by ebaines View Post
    #6 is easier than you think! You have a right angle triangle with one node from the center of the sphere , another at the center of the slice, and a third at the intersection of the slice and the edge of the spehere. You know the values for the radius of the sphere and the circle, so use Pythagoras to find x.

    Click image for larger version. 

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    #7 is so obvious you're just not seeing it. It would be similar to a problem like this: if x=y, and x=8, what is y?
    Thanks for #6.

    I did not read #7 correctly (or, I should say I didn't read it "completely"). A lot of superfluous info in there, and I read only the wrong information.
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