How to Solve a Common-Tangent Problem
How to Determine the Length of an Arc
How to Identify Radii, Chords, and Diameters

What You Need to Know About a Circle's Radius and Chords

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.

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