Formulas for Secants & Chords
Formulas for Lengths & Angles of Chords & Secants
This video is a quick review of the formulas for chords and secants. For lengths of chords and secants we've got ab=cd and a(a+b)=c(c+d). For angles between chords and secants, we've got the "half the sum" and "half the difference" formulas. This video focuses on how to remember all these, and how to keep chords and secants straight.
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!
Secant Angle Problems (for Circles)
This video focuses on the problems where you have two secants and the intercepted arcs between them. You then use the "half the difference" formula to find the missing angle or arc.
Secant Length Problems (in Circles)
This video focuses on how to find the length of secants and secant segments using the ab=bc formula, sometimes written as a(a+b)=c(c+d). This video also covers the most common type of error students make on these, namely not making sure that you're plugging the right length into the formula.