Results 1 to 8 of 8

Math Help - Disjoint Circles

  1. #1
    Newbie
    Joined
    Jan 2010
    Posts
    13

    Disjoint Circles

    How can prove that?
    Let C be a collection of disjoint circles in the plane. Show that there is a line that passes through the origin and not any of these tangent circles.


    THANKS!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by rhemo View Post
    How can prove that?
    Let C be a collection of disjoint circles in the plane. Show that there is a line that passes through the origin and not any of these tangent circles.


    THANKS!
    I don't see why this is true. Why not the infinite collection of circle centered on O with radius \frac{1}{n},\text{ }n\in\mathbb{N}?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2010
    Posts
    13
    Again:

    Let C a collection of disjoint circles in the plane. Show that there is a line that passes through the origin and is not tangent to any of these circles

    (Excuse-me my bad English, I don't speak that language)
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by rhemo View Post
    How can prove that?
    Let C be a collection of disjoint circles in the plane. Show that there is a line that passes through the origin and not any of these tangent circles.
    I think that by disjoint circles the OP means that to circles share neither a point nor an interior point, in the sense of disks.
    If that is the case, then the collection is countable. WHY?
    If a circle in the plane does not contain the origin as a point or interior point then there is at least one and at most two tangents to the circle that contain the origin.
    There are uncountably many lines through the origin.
    Can you finish?
    Follow Math Help Forum on Facebook and Google+

  5. #5
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Plato View Post
    I think that by disjoint circles the OP means that to circles share neither a point nor an interior point, in the sense of disks.
    If that is the case, then the collection is countable. WHY?
    If a circle in the plane does not contain the origin as a point or interior point then there is at least one and at most two tangents to the circle that contain the origin.
    There are uncountably many lines through the origin.
    Can you finish?
    Clearly, each of this circles can be uniquely identified with a unique point of the rationals, thus it is countable. But, I have never heard it meant that way before? I thought usually disjoint meant what you said, and concentric.
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1573
    Awards
    1
    Quote Originally Posted by Drexel28 View Post
    But, I have never heard it meant that way before? I thought usually disjoint meant what you said, and concentric.
    The poster said he/she is not an Enghish speaker.
    Just replace the word circle with the word closed disk.
    Follow Math Help Forum on Facebook and Google+

  7. #7
    MHF Contributor Drexel28's Avatar
    Joined
    Nov 2009
    From
    Berkeley, California
    Posts
    4,563
    Thanks
    21
    Quote Originally Posted by Plato View Post
    The poster said he/she is not an Enghish speaker.
    Just replace the word circle with the word closed disk.
    That makes sense
    Follow Math Help Forum on Facebook and Google+

  8. #8
    Newbie
    Joined
    Jan 2010
    Posts
    13
    Thanks a lot!!!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. [SOLVED] Set related question ... find out if disjoint of not disjoint ...
    Posted in the Discrete Math Forum
    Replies: 7
    Last Post: July 9th 2011, 02:26 AM
  2. disjoint subsets
    Posted in the Discrete Math Forum
    Replies: 1
    Last Post: May 18th 2010, 04:28 PM
  3. Prove that every rigid motion transforms circles into circles
    Posted in the Differential Geometry Forum
    Replies: 4
    Last Post: February 11th 2010, 06:00 PM
  4. Replies: 2
    Last Post: October 6th 2009, 08:04 AM
  5. disjoint intervals
    Posted in the Differential Geometry Forum
    Replies: 2
    Last Post: September 10th 2009, 08:43 AM

Search Tags


/mathhelpforum @mathhelpforum