Skip to content

Puzzle: diameter ≥ chord

May 10, 2009 am31 12:28 am

How could we show/prove that the diameter is the longest chord in a circle?

(What prior knowledge is necessary to support your answer?)

Advertisements
2 Comments leave one →
  1. David Petersen permalink
    May 10, 2009 am31 2:07 am 2:07 am

    triangle inequality

  2. May 12, 2009 am31 8:55 am 8:55 am

    In any triangle, the length of any one side is no more than the sum of the lengths of the other two sides, with equality only for a degenerate triangle (a line).

    Given a chord, create a triangle using the chord as one side, and using radii for the other two sides (connecting the ends of the chord to the center).

    Voila. The length of any chord is no more than twice the radius of the circle, and the length of a chord through the center is equal to twice the radius of the circle.

    [scrolls upward…d’oh! what David Peterson said! it amounts to the same thing….]

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

%d bloggers like this: