Results 1 to 3 of 3

Math Help - Prove that line DF is parallel to BC...

  1. #1
    Junior Member
    Joined
    Oct 2012
    From
    Ohio
    Posts
    48

    Prove that line DF is parallel to BC...

    Let ABC be a triangle. Let K be a circle that contains B and C, intersects side AB at a point D between A and B, and intersects side AC at a point E betwen A and C. Let L be a circle that contains D and E and is tangent to line AB. Also assume that L intersects AE at a point F between A and E. Prove that line DF is parallel to line BC.

    I've tried everything, any help please?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor
    Joined
    Sep 2012
    From
    Australia
    Posts
    3,607
    Thanks
    591

    Re: Prove that line DF is parallel to BC...

    Hey TimsBobby2.

    For these kinds of problems, drawing a diagram is a good place to start since visual cues are often seen and they bring more information than just a purely algebraic formulation would.

    Have you drawn a diagram for this problem?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    614
    Thanks
    249

    Re: Prove that line DF is parallel to BC...

    I agree 100% with the previous posting. With the availability of good free/cheap dynamic geometry programs, there's really no excuse not to draw a figure. When you said "K contains B and C", I thought you meant B and C were interior to K or on K. A dynamic geometry program rapidly convinces you that B and C must be on K.

    Here's a drawing of your problem together with a solution:

    Prove that line DF is parallel to BC...-mhfgeometry.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 7
    Last Post: October 17th 2012, 08:56 PM
  2. Replies: 1
    Last Post: August 30th 2012, 12:56 PM
  3. Replies: 1
    Last Post: March 14th 2010, 01:22 PM
  4. Replies: 5
    Last Post: November 4th 2009, 06:49 PM
  5. Replies: 9
    Last Post: July 31st 2009, 05:39 AM

Search Tags


/mathhelpforum @mathhelpforum