Concept Byte: Exploring Chords and Secants

Use With Lesson 12-4

TECHNOLOGY

Activity 1

Construct ⊙ A circle dot eh  and two chords B C ¯ b c bar  and D E ¯ d e bar  that intersect at F.

1. Measure B F ¯ , F C ¯ , E F ¯ , b f bar , comma . f c bar , comma . e f bar , comma  and F D ¯ . f d bar , .
2. Use the calculator program of your software to find B F · F C b f middle dot f c  and E F · F D . e f middle dot f d .
3. Manipulate the lines. What pattern do you observe in the products?
4. Make a Conjecture What appears to be true for two intersecting chords?

Activity 2

A secant is a line that intersects a circle in two points. A secant segment is a segment that contains a chord of the circle and has only one endpoint outside the circle. Construct a new circle and two secants D G ↔ modified d g with left right arrow above  and D E → d e vector  that intersect outside the circle at point D. Label the intersections with the circle as shown.

5. Measure D G ¯ , D F ¯ , D E ¯ , d g bar , comma . d f bar , comma . d e bar , comma  and D B ¯ . d b bar , .
6. Calculate the products D G · D F d g middle dot d f  and D E · D B . d e middle dot d b .
7. Manipulate the lines. What pattern do you observe in the products?
8. Make a Conjecture What appears to be true for two intersecting secants?

Activity 3

Construct ⊙ A circle dot eh  with tangent D G ¯ d g bar  perpendicular to radius A G ¯ eh g bar  and secant D E ¯ d e bar  that intersects the circle at B and E.

9. Measure D G ¯ , D E ¯ , d g bar , comma . d e bar , comma  and D B ¯ . d b bar , .
10. Calculate the products ( D G ) 2 open d g , close squared  and D E · D B . d e middle dot d b .
11. Manipulate the lines. What pattern do you observe in the products?
12. Make a Conjecture What appears to be true for the tangent segment and secant segment?

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