Results 1 to 4 of 4
Like Tree1Thanks
  • 1 Post By johng

Math Help - Chordal quadrileteral problem

  1. #1
    Newbie
    Joined
    Jan 2013
    From
    Netherlands
    Posts
    15
    Thanks
    1

    Chordal quadrileteral problem

    Hello everyone,

    I'm having a bit of trouble understanding the following proof of this problem:
    Chordal quadrileteral problem-schermafbeelding-2013-03-18-om-17.16.37.png"Prove that ABFE is a chordal quadrileteral."

    Proof given by solutions book:

    "Angle A = 1/2*arc CD - 1/2*arc ED = 90o- 1/2*arc ED.
    Angle EFC = 1/2*arc EC = 1/2*(arc CD - arc ED) = 90o- 1/2*arc ED.
    => Angle A = Angle EFC.
    Angle A + Angle EFB = Angle EFC + Angle EFB = 180o.
    Thus ABFE is a chordal quadrileteral."

    I do understand the logic of the proof and the whole conclusion, however I am stuck at the beginning, where the angles are given as arcs. Could anybody explain to me how this is done?

    Thanks in advance,
    Tom
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor

    Joined
    Aug 2006
    Posts
    18,959
    Thanks
    1783
    Awards
    1

    Re: Chordal quadrileteral problem

    Quote Originally Posted by tomkoolen View Post
    Hello everyone,

    I'm having a bit of trouble understanding the following proof of this problem:
    Click image for larger version. 

Name:	Schermafbeelding 2013-03-18 om 17.16.37.png 
Views:	5 
Size:	247.3 KB 
ID:	27586"Prove that ABFE is a chordal quadrileteral."

    Proof given by solutions book:

    "Angle A = 1/2*arc CD - 1/2*arc ED = 90o- 1/2*arc ED.
    Angle EFC = 1/2*arc EC = 1/2*(arc CD - arc ED) = 90o- 1/2*arc ED.
    => Angle A = Angle EFC.
    Angle A + Angle EFB = Angle EFC + Angle EFB = 180o.
    Thus ABFE is a chordal quadrileteral."

    I do understand the logic of the proof and the whole conclusion, however I am stuck at the beginning, where the angles are given as arcs. Could anybody explain to me how this is done?

    Thanks in advance,
    Tom
    Please define chordal quadrileteral.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Jan 2013
    From
    Netherlands
    Posts
    15
    Thanks
    1

    Re: Chordal quadrileteral problem

    It is in America more often called cyclic quadrilateral; a quadrilateral with all of its vertices on a circle.
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Dec 2012
    From
    Athens, OH, USA
    Posts
    709
    Thanks
    294

    Re: Chordal quadrileteral problem

    Hi,

    In a circle an arc angle is the length of the arc divided by the radius of the circle (formula s=r\theta). Equivalently, an arc angle is the measure of the "central" angle; i.e. the angle from the center of the circle with endpoints the endpoints of the arc. Here's the theorem which is the first line of your proof:

    Chordal quadrileteral problem-mhfgeometry18chords.png
    Thanks from tomkoolen
    Follow Math Help Forum on Facebook and Google+

Search Tags


/mathhelpforum @mathhelpforum