Geometry For Dummies
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When you’re working with a circle, there are five important theorems that you need to know about the properties of the circle’s radii and chords. (There are really just three ideas; but two of the theorems work in both directions which brings the total to five):

Segment <i>PG</i> is a chord, segment <i>AB</i> is the diameter, and segment <i>OC</i> is the radiu
Segment PG is a chord, segment AB is the diameter, and segment OC is the radius of this circle.

  • Radii size: All radii of a circle are congruent.

  • Perpendicularity and bisected chords:

    • If a radius is perpendicular to a chord, then it bisects the chord.

    • If a radius bisects a chord (that isn’t a diameter), then it’s perpendicular to the chord.

  • Distance and chord size:

    • If two chords of a circle are equidistant from the center of the circle, then they’re congruent.

    • If two chords of a circle are congruent, then they’re equidistant from its center.

About This Article

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About the book author:

Mark Ryan has taught pre-algebra through calculus for more than 25 years. In 1997, he founded The Math Center in Winnetka, Illinois, where he teaches junior high and high school mathematics courses and standardized test prep classes. He also does extensive one-on-one tutoring. He is a member of the Authors Guild and the National Council of Teachers of Mathematics. Ryan is the author of Calculus For Dummies, Calculus Workbook For Dummies, and Geometry Workbook For Dummies.

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