Results 1 to 2 of 2

Math Help - A geometric identity I need

  1. #1
    Junior Member
    Joined
    Jun 2010
    Posts
    54

    A geometric identity I need

    My instructor for complex analysis used the following geometric fact without giving proof, and I'm wondering if anyone out there could help me see a good proof of this:

    Let A, B, C be collinear, and suppose B and C lie on a circle with center O. Draw a line from A to the circle so that it is tangent to the circle at a point P on the circle. Prove that

    |AP|^2=|AB||AC|

    I'd appreciate any solutions or hints. I am hoping for a more-or-less "pure geometry" proof, rather than some kind of coordinate-based or vector-based proof, but if you find this inconvenient, I'd be happy with any solution.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Jul 2012
    From
    INDIA
    Posts
    831
    Thanks
    209

    Re: A geometric identity I need

    A geometric identity I need-chords.png
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 0
    Last Post: September 5th 2012, 11:21 PM
  2. Replies: 3
    Last Post: August 24th 2012, 03:17 PM
  3. Replies: 6
    Last Post: May 23rd 2011, 02:36 AM
  4. Geometric Progression or Geometric Series
    Posted in the Math Topics Forum
    Replies: 8
    Last Post: October 8th 2009, 07:31 AM
  5. Replies: 2
    Last Post: January 23rd 2007, 08:47 AM

Search Tags


/mathhelpforum @mathhelpforum