I wrote this worksheet so that my students could derive the relationship between the lengths formed when two chords of a circle intersect inside of a circle. Typically, this relationship is expressed in texts as ab = cd, where one chord is made up of segments of lengths a and b, and the second is made up of lengths c and d.
Students use similar triangles to develop the formula. This worksheet "holds their hands" through the process so that they develop it step-by-step. Some of the steps give them hints along the way, and some steps suggest correct answers in places where I have found students often get stuck.
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: circles, chords, formulas, similar triangles, inscribed angles, intercepted arcs, Jonnard