Results 1 to 4 of 4

Math Help - Construction help!

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    US
    Posts
    20

    Construction help!

    Given a line, L and two points, A & B not on the line, construct a circle which contains both points and is tangent to
    the given line.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    826
    Thanks
    209

    Re: Construction help!

    Construction help!-08-apr-13-2.png
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Senior Member
    Joined
    Feb 2013
    From
    Saudi Arabia
    Posts
    440
    Thanks
    86

    Re: Construction help!

    The lines AB and L intersect at a fixed point P.
    The circle we search has centre at O . and the line L is tangent to this circle at the point Q.
    According to a well known theorem of the Euclidean Geometry (PA) X (PB) = (PQ)^2 therefore PQ =SQRROOT[(PA) X (PB)]
    this expression defines the position of the point of tangency Q along the line L . The centre of the circle is the intersection point O of the perpendicular bisector of AB and the perpendicular line to the line L at Q. OA =OB =OQ = r is the radius of the circle .

    MINOAS
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,605
    Thanks
    1574
    Awards
    1

    Re: Construction help!

    Quote Originally Posted by Jammix View Post
    Given a line, L and two points, A & B not on the line, construct a circle which contains both points and is tangent to the given line.
    Quote Originally Posted by MINOANMAN View Post
    The lines AB and L intersect at a fixed point P.
    The circle we search has centre at O . and the line L is tangent to this circle at the point Q.
    According to a well known theorem of the Euclidean Geometry (PA) X (PB) = (PQ)^2 therefore PQ =SQRROOT[(PA) X (PB)]
    this expression defines the position of the point of tangency Q along the line L . The centre of the circle is the intersection point O of the perpendicular bisector of AB and the perpendicular line to the line L at Q. OA =OB =OQ = r is the radius of the circle .

    The original question contains a mistake.
    What if your point is between A~\&~B, that is A-P-B~? If so the no such circle exists.

    So it must be stated that A~\&~B are on the same side of \ell.

    But then it may be that \overleftrightarrow {AB} \cap \ell  = \emptyset, parallel. In which case P does not exist.
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. NFA construction
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: March 3rd 2010, 01:35 PM
  2. Construction: How?
    Posted in the Geometry Forum
    Replies: 1
    Last Post: May 3rd 2009, 03:27 PM
  3. Construction help
    Posted in the Geometry Forum
    Replies: 2
    Last Post: April 27th 2009, 05:21 AM
  4. I need help with a construction.
    Posted in the Geometry Forum
    Replies: 1
    Last Post: April 26th 2009, 12:28 PM
  5. Construction
    Posted in the Geometry Forum
    Replies: 0
    Last Post: October 11th 2005, 01:56 PM

Search Tags


/mathhelpforum @mathhelpforum