Chords of Circles

Summary of Chord Theorems (free)

There are so many chord theorems that it's hard to keep track! So I quickly introduce them all in this video in case you need to review, then the videos afterwards cover the nuances and example problems in depth. This video is also a good place to start for proofs, to give you ideas which theorems cover chords.

Chord Problems with Congruent Arcs

This video covers one of the many types of chord problems: the type using the theorem that congruent arcs have congruent chords, and vice versa. Also covered are more complicated problems where the congruent arcs theorem is mixed in with older material, like central and inscribed angles.

Chord Problems Involving Triangles

There are so many types of chord problems, but this video covers just the type where chords form triangles inside of circles: inscribed triangles, inscribed triangles in semicircles, triangles formed by intersecting chords... If there's a triangle somewhere in a circle, this video is a good place to start.

Equidistant Congruent Chords

Examples involving two theorems: One theorem says chords equidistant from the center of a circle are congruent. The other theorem says that if a chord hits a diameter at a right angle it bisects the chord, and vice versa. The takeaway: If you see a "T" shape inside a circle, you've probably got a right angle and some congruence.

Segment Lengths of Intersecting Chords (ab=cd)

These problems are the ones where you have two chords intersecting, and if you multiply the two halves of one chord you'll get the same product as when you multiply the halves of the other chord. Depending on how you label things: ab=cd or ad=bc, or ac=db.

Chord Angles and Intercepted Arcs

At this point in the circles chapter, you already know what to do when a missing angle is at the center of a circle (central angle) or on the edge (inscribed angles). But what if it's an angle between two chords that's not on the edge or in the middle? Well, it's "half the sum" of the two intercepted arcs, of course!

Circle Chord Proofs

In previous videos we saw all the different chord theorems. Now it's time to put a few of them into practice in proofs! We'll even prove a couple of chord theorems, which is a popular homework question.