Results 1 to 7 of 7

Math Help - Two secants to a circle

  1. #1
    Newbie
    Joined
    Sep 2011
    Posts
    10

    Two secants to a circle


    BA^2 + CD^2 = 16
    PA = 1.25
    PC = 0.75
    AB? CD?

    Thank you!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Two secants to a circle

    What have you tried?
    Do you know the 'intersecting secant theorem'?
    Look here:
    Intersecting Secant Theorem - Math Open Reference
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2011
    Posts
    10

    Re: Two secants to a circle

    Quote Originally Posted by Siron View Post
    What have you tried?
    Do you know the 'intersecting secant theorem'?
    Look here:
    Intersecting Secant Theorem - Math Open Reference
    Thanks, I didn't know about this theorem.
    However I can't resolve the problem anyway, in fact I only know something about AB and CD and not about PB and PD. What do you think?
    Follow Math Help Forum on Facebook and Google+

  4. #4
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Two secants to a circle

    Along the theorem:
    PA\cdot PB = PC \cdot PD
    But we can write PB=PA+AB and PD=PC+DC therefore:
    PA\cdot (PA+AB)=PC \cdot (PC+DC)
    \Leftrightarrow (PA)^2+PA\cdot AB=(PC)^2+PC\cdot DC
    \Leftrightarrow DC=\frac{(PA)^2+PA\cdot AB - (PC)^2}{PC} (1)

    You have given PA=1,25 and PC=0,75 so you can substitute them in (1). You have also given:
    (AB)^2+(DC)^2=16 (2)

    If we susbtitute (1) in (2) we get:
     (AB)^2+\left[\frac{(PA)^2+PA\cdot AB - (PC)^2}{PC}\right]^2=16

    If you have substituted the given values for PC and PA into this equation then you will have a quadratic equation in one variable AB which you can solve (you will get two solutions but offcourse you have to reject the negative one because the lenght of a side can't be negative).
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Sep 2011
    Posts
    10

    Re: Two secants to a circle

    Wow, very nice explanation, thank you very much!
    Last thing: I looked for a demonstration of the intersecting secant theorem but I couldn't find one, how can I get to that theorem?
    Follow Math Help Forum on Facebook and Google+

  6. #6
    MHF Contributor Siron's Avatar
    Joined
    Jul 2011
    From
    Norway
    Posts
    1,250
    Thanks
    20

    Re: Two secants to a circle

    Quote Originally Posted by goby View Post
    Wow, very nice explanation, thank you very much!
    Last thing: I looked for a demonstration of the intersecting secant theorem but I couldn't find one, how can I get to that theorem?
    You're welcome! Did you find AB and CD?
    If you want a proof then you can take a look here:
    http://www.mathforamerica.org/c/docu...e=DLFE-112.pdf
    Follow Math Help Forum on Facebook and Google+

  7. #7
    Newbie
    Joined
    Sep 2011
    Posts
    10

    Re: Two secants to a circle

    Sure! I solved the equation and I get AB = 1,44 so CD is 3.73. Thank you again!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Can someone help me with secants and tangents?
    Posted in the Pre-Calculus Forum
    Replies: 6
    Last Post: April 18th 2011, 06:52 AM
  2. Secants
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 22nd 2009, 06:46 AM
  3. Slopes of Secants
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: May 21st 2009, 11:47 AM
  4. Secants and Tangents
    Posted in the Geometry Forum
    Replies: 2
    Last Post: May 16th 2009, 10:27 PM
  5. Tangent and secants
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: March 14th 2009, 02:54 PM

Search Tags


/mathhelpforum @mathhelpforum