Results 1 to 3 of 3

Math Help - Angle sbutended by a chord in a circle

  1. #1
    Newbie
    Joined
    Sep 2010
    Posts
    2

    Angle sbutended by a chord in a circle

    I was going through the proof of a theorem which says, "The angle subtended by a chord at the center of a circle is twice the angle subtended by it elsewhere on the circle."

    This was proved by considering three cases: when the arc forming the chord was:
    1) a minor arc
    2) a major arc
    3) a semi circle

    I realized that the following scenario has been avoided, which is what I'm trying to prove:

    Angle sbutended by a chord in a circle-1.png


    Prove that: Angle AOB = 2 * Angle APB

    You see, the textbook very cleverly takes the point P above the point O, which allows joining O and P, and the problem is easily solved by using the property of exterior angles.

    Is this interpretation right? If not, why? If yes, how is it to be proved?

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

  2. #2
    A riddle wrapped in an enigma
    masters's Avatar
    Joined
    Jan 2008
    From
    Big Stone Gap, Virginia
    Posts
    2,551
    Thanks
    11
    Awards
    1
    Hi ankush,

    Check this out: Inscribed-Central Angle Proof
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2010
    Posts
    2
    Well, thank you, but this has already been covered in the book. Besides, the animation you provided talks about an arc, not a chord (though it works out to be the same thing).

    Could you please comment on the figure I posted?
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 3
    Last Post: October 18th 2010, 12:28 PM
  2. Chord and Circle
    Posted in the Geometry Forum
    Replies: 2
    Last Post: February 7th 2010, 07:22 PM
  3. Finding the angle where the chord subtends
    Posted in the Trigonometry Forum
    Replies: 1
    Last Post: August 17th 2009, 03:02 AM
  4. Circle From Included Angle and Chord Length
    Posted in the Geometry Forum
    Replies: 5
    Last Post: July 17th 2009, 01:50 PM
  5. Circle and Chord
    Posted in the Geometry Forum
    Replies: 1
    Last Post: March 23rd 2007, 05:10 AM

Search Tags


/mathhelpforum @mathhelpforum