Results 1 to 4 of 4

Math Help - At least two circles tangent to y axis with nonempty intersection

  1. #1
    Junior Member
    Joined
    Nov 2012
    From
    Ukraine
    Posts
    43

    At least two circles tangent to y axis with nonempty intersection

    Hi.

    Here is a problem I've been trying to solve for some time now. Maybe you could help me.
    We have two sets
    \mathcal {Q} is a set of those circles in the plane such that for any x \in \mathbb{R} there exists a circle O \in \mathcal {Q} which intersects x axis in (x,0).


    \mathcal {T} is a set of those circles in the plane such that for any x \in \mathbb{R} there exists a circle O \in \mathcal {T} which is tangent to x axis in (x,0).
    Last edited by wilhelm; January 11th 2013 at 06:23 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,651
    Thanks
    602

    Re: At least two circles tangent to y axis with nonempty intersection

    Hey wilhelm.

    Do you just have to show existence of such circles?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    Nov 2012
    From
    Ukraine
    Posts
    43

    Re: At least two circles tangent to y axis with nonempty intersection

    That's right. I think that maybe we could somehow identify each circle with a different rational number and this would mean that there is at most countably many disjoint circles in the plane but uncountably many points on x axis, so at least two must intersect. If this reasoning is right, it holds for both sets, doesn't it?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Jan 2013
    From
    http://www.dvdsetoutlet.com
    Posts
    10
    Thanks
    1

    Re: At least two circles tangent to y axis with nonempty intersection

    If this reasoning is right, it holds for both sets, doesn't it?




    __________________
    Your DVD Zone, Take Your Choice without Any Doubt on The Newsroom Season 1 DVD
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: May 12th 2012, 11:37 PM
  2. Area of intersection of two circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: December 13th 2011, 07:36 PM
  3. intersection of circles
    Posted in the Algebra Forum
    Replies: 9
    Last Post: March 31st 2011, 01:57 PM
  4. Replies: 2
    Last Post: April 2nd 2010, 05:01 AM
  5. Intersection of circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 21st 2009, 07:20 AM

Search Tags


/mathhelpforum @mathhelpforum