10.3: Circle Product Theorems
This activity is intended to supplement Geometry, Chapter 9, Lesson 6.
ID: 12512
Time Required: 20 minutes
Activity Overview
Students will use dynamic models to find patterns. These patterns are the ChordChord, SecantSecant, and SecantTangent Theorems.
Topic: Circles
 ChordChord, SecantSecant, and the SecantTangent Product Theorems
Teacher Preparation and Notes
 This activity was written to be explored with the Cabri Jr. application on the TI84.
 To download Cabri Jr, go to http://www.education.ti.com/calculators/downloads/US/Software/Detail?id=258#.
 To download the calculator files, go to http://www.education.ti.com/calculators/downloads/US/Activities/Detail?id=12512 and select PRODUC1PRODUC5.
Associated Materials
 Student Worksheet: Circle Product Theorems http://www.ck12.org/flexr/chapter/9694, scroll down to the third activity.
 Cabri Jr. Application
 PRODUC1.8xv, PRODUC2.8xv, and PRODUC3.8xv
Problem 1 – ChordChord Product Theorem
Students will begin this activity by investigating the intersection of two chords and the product of the length of the segments of one chord and the product of the length of the segments of the other chord.
Students will be asked to collect data by moving point
As an extension, prove the chordchord product theorem using similar triangles.
Problem 2 – SecantSecant Product Theorem
Students will investigate the intersection of two secants and the product of the lengths of one secant segment and its external segment and the product of the lengths of the other secant segment and its external segment.
Students will be asked to collect data by moving point
As an extension, prove the secantsecant product theorem using similar triangles.
Problem 3 – SecantTangent Product Theorem
Students will investigate the intersection of the product of the lengths of one secant segment and its external segment and the square of the tangent segment.
Students will be asked to collect data by moving point
As an extension, prove the secanttangent product theorem using similar triangles.
Problem 4 – Application of the Product Theorems
Students will be asked to apply what they learned in Problems 1–3 to solve a few problems.
Solutions
1. Sample answers:
Position 







1  2.70  0.99  1.51  1.78  2.67  2.68 
2  2.51  1.05  1.38  1.90  2.63  2.62 
3  2.93  0.91  1.80  1.49  2.67  2.68 
4  1.80  1.08  2.51  0.77  1.94  1.93 
2. They are equal.
3. equal
4. Sample answers:
Position 







1  5.94  3.82  6.65  3.42  22.69  22.74 
2  4.85  3.16  5.85  2.62  15.33  15.33 
3  4.03  2.75  5.32  2.09  11.08  11.12 
4  7.47  4.96  7.92  4.68  37.05  37.07 
5. They are equal.
6. equals
7. Sample answers:
Position 






1  4.22  6.13  2.90  17.81  17.77 
2  3.42  5.40  2.16  11.70  11.66 
3  2.45  4.56  1.32  6.00  6.02 
4  9.46  11.21  7.98  89.49  89.46 
8. They are equal.
9. equals
10. 6
11.
12.
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