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?)
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triangle inequality
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….]