10.3: Circle Product Theorems
This activity is intended to supplement Geometry, Chapter 9, Lesson 6.
Problem 1 – ChordChord Product Theorem
Start the Cabri Jr. application by pressing the APPS key and selecting Cabri Jr. Open the file INSCRIB1 by pressing
1. Move point
Position 







1  
2  
3  
4 
2. What do you notice about the products
3. If two chords intersect in the interior of a circle, then the product of the lengths of the segments of one chord is ____________ to the product of the lengths of the segments of the other chord.
Problem 2 – SecantSecant Product Theorem
Open the file PRODUC2. You are given circle
4. Move point
Position 







1  
2  
3  
4 
5. What do you notice about the products
6. If two secant segments share the same endpoint outside of a circle, then the product of the lengths of one secant segment and its external segment ___________ the product of the lengths of the other secant segment and its external segment.
Problem 3 – SecantTangent Product Theorem
Open the file PRODUC3. You are given circle
7. Move point
Position 






1  
2  
3  
4 
8. What do you notice about the products
9. If a secant segment and a tangent segment share an endpoint outside of a circle, then the product of the lengths of the secant segment and its external segment _________ the square of the length of the tangent segment.
Problem 4 – Application of Product Theorems
10. Find the value of
11. Find the value of
12. Find the value of
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