I have found that instead of giving a lecture on the angles and lengths formed by intersecting chords, secants, and tangents, it's more productive to have my students work together during the class and problem-solve.
These formulas are sometimes called the power theorems.
I do open the class with a mini-lesson (about 10 minutes) to show them what they'll be doing, and then when I set them to work, they have a good 45 minutes to an hour to work together.
Students earlier developed the formulas for chords, secants, and tangents by use of conjecture; on this worksheet, they apply the formulas to a variety of contexts.
I recommend you print out the last page on colored paper as a reference page, and then the first 3 pages serve as the worksheet (If you just photocopy all 4 pages, they have to flip back and forth)
I use this activity within cooperative groups, and I circulate to make sure they are getting the purpose of the questions.
The file includes spiral review problems.
This worksheet is intended to be written on directly.
Please download the pdf preview file first, so you can see exactly what's included; the product file is a word document, which you may personalize for your students.
Keywords: power theorems, secant-secant power theorem, secant-secant power theorem, circle power theorems, Jonnard