<img src="https://d5nxst8fruw4z.cloudfront.net/atrk.gif?account=iA1Pi1a8Dy00ym" style="display:none" height="1" width="1" alt="" />
Dismiss
Skip Navigation

10.3: Circle Product Theorems

Difficulty Level: At Grade Created by: CK-12
Turn In

This activity is intended to supplement Geometry, Chapter 9, Lesson 6.

Problem 1 – Chord-Chord Product Theorem

Start the Cabri Jr. application by pressing the APPS key and selecting CabriJr. Open the file INSCRIB1 by pressing Y=, selecting Open..., and selecting the file. In PRODUC1, you are given circle O and two chords AB and CD that intersect at point X. You are also given the lengths AX, BX, CX, and DX.

1. Move point A to four different points and collect the data in the table below and calculate the products AXBX and CXDX.

Position AX BX CX DX AXBX CXDX
1
2
3
4

2. What do you notice about the products AXBX and CXDX?

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 – Secant-Secant Product Theorem

Open the file PRODUC2. You are given circle O and two chords AB and CD that intersect at point X. You are also given the lengths AX, BX, CX, and DX.

4. Move point A to four different points and collect the data in the table below and calculate the products AXBX and CXDX.

Position AX BX CX DX AXBX CXDX
1
2
3
4

5. What do you notice about the products AXBX and CXDX?

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 – Secant-Tangent Product Theorem

Open the file PRODUC3. You are given circle O and two chords AB and CD that intersect at point X. You are also given the lengths AX, CX, and DX.

7. Move point A to four different points and collect the data in the table below and calculate AX2 and CXDX.

Position AX CX \begin{align*}DX\end{align*} \begin{align*}AX^2\end{align*} \begin{align*}CX \cdot DX\end{align*}
1
2
3
4

8. What do you notice about the products \begin{align*}AX^2\end{align*} and \begin{align*}CX \cdot DX\end{align*}?

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 \begin{align*}x\end{align*}.

11. Find the value of \begin{align*}x\end{align*}.

12. Find the value of \begin{align*}x\end{align*}.

Notes/Highlights Having trouble? Report an issue.

Color Highlighted Text Notes
Please to create your own Highlights / Notes
Show More

Image Attributions

Show Hide Details
Description
Subjects:
Grades:
Date Created:
Feb 23, 2012
Last Modified:
Nov 03, 2014
Files can only be attached to the latest version of section
Please wait...
Please wait...
Image Detail
Sizes: Medium | Original
 
TI.MAT.ENG.SE.1.Geometry.10.3
Here