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

By Mark Ryan

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):

  • 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.