11-6 Segment Relationships in Circles

[Pages:3]Name ________________________________________ Date __________________ Class__________________

LESSON Reteach

11-6 Segment Relationships in Circles

Chord-Chord Product Theorem

If two chords intersect in the interior of a circle, then the products of the lengths of the segments of the chords are equal.

AE EB = CE ED

Find the value of x and the length of each chord.

HL LJ = KL LM

Chord-Chord Product Thm.

4 9 = 6 x

HL = 4, LJ = 9, KL = 6, LM = x

36 = 6x

Simplify.

6 = x

Divide each side by 6.

HJ = 4 + 9 = 13

KM = 6 + x

= 6 + 6 = 12

Find the value of the variable and the length of each chord.

1.

2.

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3.

4.

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Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

11-46

Holt Geometry

Name ________________________________________ Date __________________ Class__________________

LESSON Reteach

11-6 Segment Relationships in Circles continued

? A secant segment is a segment of a secant with at least one endpoint on the circle.

AE is a secant segment.

BE is an external secant segment.

? An external secant segment is the part of the secant segment that lies in the exterior of the circle.

? A tangent segment is a segment of a tangent with one endpoint on the circle.

ED is a tangent segment.

If two segments intersect outside a circle, the following theorems are true.

Secant-Secant Product Theorem The product of the lengths of one secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment.

whole outside = whole outside AE BE = CE DE

Secant-Tangent Product Theorem The product of the lengths of the secant segment and its external segment equals the length of the tangent segment squared.

whole outside = tangent2 AE BE = DE2

Find the value of the variable and the length of each secant segment.

5.

6.

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Find the value of the variable. 7.

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8.

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Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

11-47

Holt Geometry

Challenge Student justifications will vary. 15. (4.5 + 2.25 3 ) inches 8.4 in.

16. (6.75 + 2.25 3 ) inches 10.6 in.

17. (9 + 2.25 3 ) inches 12.9 in.

18. 2.25(n - 1) + 2.25 3 , or 2.25(n - 1 +

3)

19. Isosceles right triangle with legs of

d

1

+

2 + (n - 1)

2

2 in.; hypotenuse

of [d(2n - 1 + 2 )] in.

Problem Solving 1. 68? 3. 110.8? 5. C

2. 76 4. 162.6? 6. J

Reading Strategies 1. 60? 3. 60?

2. 81? 4. 31?

LESSON 11-6

Practice A

1. C

2. B

3. A

4. x = 6; JL = 16; KM = 17

5. y = 25; PR = 29; QS = 20

6. 9.75 m

7. a = 3.8; VT = 11; VX = 8.8

8. z = 4; BD = 6; BF = 6

9. 12

10. 6

Practice B 1. x = 1; AD = 6; BE = 9 2. y = 7; FH = 8.3; GI = 9.4 3. z = 7; PS = 9.4; TR = 9.4 4. m = 4.5; UW = 8.5; VX = 9 5. x = 4.5; BD = 9.5; FD = 9.5 6. y = 11.5; GJ = 21; GK = 17.5 7. z = 19; SQ = 18; SU = 28

8. n = 8.25; CE = 20.25; CF = 27

9. 1.5

10. 10

11. 78

12. 70

Practice C 1. 2 3. 13.3 5. 7.1 7. 8.4 9. 16.5; 16.8

2. 5 4. 7.2 6. 1.2 8. 15.7 10. 40.5

Reteach

1. y = 7; RS = 10; TV = 10

2. x = 10; DF = 16; GH = 17

3. z = 7.5; JL = 11; MN= 11.5

4. x = 2.5; AC = 18.5; DE = 13

5. x = 2; NQ = 12; NS = 8

6. z = 12.25; TV = 20.25; WV = 18

7. 8

8. 7.5

Challenge

1. RS ; OS ; OH

2. OH is a tangent segment of circle C, OR

is a secant segment, and OS is its external secant segment. So (OH)2 = OR x OS.

3. 140.7 mi

4. 212.1 mi

5. OH 1.5 x OS

6. 3.9 mi

7. 17.3 mi 8. 0.7 ft, or about 8 in. 9. 11.4 mi

Problem Solving 1. 24.5 3. A 5. D

2. 20 4. H 6. F

Reading Strategies 1. 2.5 3. 8 5. 7

2. 8 4. 16 6. 24

Original content Copyright ? by Holt McDougal. Additions and changes to the original content are the responsibility of the instructor.

A40

Holt Geometry

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