Thursday, April 18, 2013

Day 131: Chords

For whatever reason, I never interpreted chords as a subset of secants. Rather, I thought of chords as a separate classification of segments, akin to tangents. What's interesting (to me anyway, I get that I'm not 'normal') is that it seems as though every math textbook ever written handles the chapter on circles different than every other text. There is SO MUCH you can discover with circles, so it ends up forcing a value judgement as to what you what students to know (and how to present it).

I went with:

  • Intersecting chords form an angle within the interior of a circle. The measure of that angle is half the sum of the two intercepted arcs.
  • If a chord is bisected at a right angle, the bisector is a diameter of the circle (I always thought that it was neat that you could find the center of a circle with 2 chords)
  • Intersecting chords break each other into 4 pieces (2 pieces each). The product of the 2 pieces of one chord is equal to the product of the 2 pieces of the other.
  • Equal chords intercept equal arcs and are equidistant to the center of the circle. Probably one of the more confusing and not obviously relevant idea. 
On the upside, I haven't had any students pronounce it with the 'ch' from 'church' sound. Progress?

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