What exactly is a chord of a circle?
Jenn, Founder Calcworkshop®, 15+ Years Experience (Licensed & Certified Teacher)
We’ll you’re in the right place because that’s what this geometry lesson is all about.
You’ll learn how to quickly find the missing measurements or indicated variables in all kinds of problems dealing with Chords and Arcs of a Circle.
So let’s get to it!
There are some fundamental theorems and definitions involving chords of a circle.
As seen in the diagram to the right, if arc AB is congruent to arc CB, then segment AB is congruent to segment CB and vice versa.
And this property holds true for congruent circles as well.
Congruent Chords and Arcs
The converse is also true. If one chord is a perpendicular bisector of another chord, then the first chord is a radius.
The same also holds if instead of a radius, it’s a diameter, as evidenced by the diagram to the right. The diameter AB is perpendicular to chord ML, and thus the diameter bisects the chord, resulting in two congruent segments (i.e., MN is equal to ML) and arcs.
Perpendicular Chord Bisector Theorem
Moreover, if two arcs are congruent, then their endpoints can be joined to form chords that are parallel. Which also means that two parallel chords intercept congruent arcs, as Math Bits Notebook nicely states.
Lastly, two chords are congruent if and only if they are equidistant from the center. This is most clearly explained in the figure below. If segments OA and OB are equal, then chords PQ and SR are also equal.
Equidistant Chord Theorem
Wow!
So what’s the big takeaway?
Congruent chords have congruent arcs, and congruent arcs have congruent chords!
In the video below you’ll see how this simple, but important fact, will help you find measures of segments, arcs, and chords. And you’ll learn how to effectively apply the Pythagorean theorem, the segment bisector definition, and the arc addition postulate along the way.
Video – Lesson & Examples
44 min
- Introduction to Video: Chords
- 00:00:29 – 5 Theorems and Definitions involving Chords of a Circle
- Exclusive Content for Member’s Only
- 00:11:07 – Find the measure of the indicated chord or arc (Examples #1-6)
- 00:26:00 – Find the measure of the indicated chord or arc (Examples #7-10)
- 00:40:06 – Answer True or False given a statement about chords or arcs of circles (Examples #11-15)
- Practice Problems with Step-by-Step Solutions
- Chapter Tests with Video Solutions
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