Results 1 to 3 of 3

Math Help - Non intersecting circles...

  1. #1
    Junior Member
    Joined
    May 2010
    Posts
    35

    Non intersecting circles...

    Ok ,

    Suppose you take two circles and they do not intersect:
    e.g

    x^2 + y^2 -6x-6y+14=0
    x^2 +y^2 +6x+4y+12 =0

    If you subtract the two equations you get a line:

    -12x-10y+2=0

    Now, if we chose any point P on this line, then the lengths of the tangents from P to each of the circles are equal?

    Why and how do we prove this?

    (I know that that if the intersected, the line would represent a common chord)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor alexmahone's Avatar
    Joined
    Oct 2008
    Posts
    1,074
    Thanks
    7

    Re: Non intersecting circles...

    Quote Originally Posted by rodders View Post
    Ok ,

    Suppose you take two circles and they do not intersect:
    e.g

    x^2 + y^2 -6x-6y+14=0
    x^2 +y^2 +6x+4y+12 =0

    If you subtract the two equations you get a line:

    -12x-10y+2=0

    Now, if we chose any point P on this line, then the lengths of the tangents from P to each of the circles are equal?

    Why and how do we prove this?

    (I know that that if the intersected, the line would represent a common chord)
    The line is the radical axis.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Junior Member
    Joined
    May 2010
    Posts
    35

    Re: Non intersecting circles...

    Thanks thats interesting.
    Is there a proof though?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 7th 2011, 04:07 PM
  2. Intersecting Circles
    Posted in the Geometry Forum
    Replies: 2
    Last Post: March 26th 2011, 11:16 PM
  3. Two circles intersecting each other...
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 25th 2010, 10:32 AM
  4. intersecting circles
    Posted in the Trigonometry Forum
    Replies: 4
    Last Post: March 14th 2009, 12:22 AM
  5. Two intersecting circles, Circle 2's...
    Posted in the Pre-Calculus Forum
    Replies: 3
    Last Post: November 16th 2008, 04:19 AM

Search Tags


/mathhelpforum @mathhelpforum