holt geometry 11-6 segment relationships in circles 4 48 14 warm up solve for x. 1. 2. 3x = 12 2 3....

Holt Geometry

11-6Segment Relationships in Circles

4

48

14

Warm UpSolve for x.

1.

2. 3x = 122

3. BC and DC are tangent to A. Find BC.

Holt Geometry

11-6Segment Relationships in Circles IN2/18 Segment Relationships in Circles

Daily Assignment:

14-5 Practice B (Due 2/17)

Journal Summary (Due 2/17)



11-1/2 Practice B (Due 2/5)

Odd Through

Summary (Last Page of Notes)

OUT

Even

Objectives: Given a circle, TSW find the lengths of segments formed by lines that intersect circles and use the lengths of segments in circles to solve problems.

Warm Up:

Starter Problems 1-3

Segment Relationships in Circles

Holt Geometry


Agenda 11-6 Warmup Problems 11-6 Presentation and Discussion 11-6 Homework Preview

Holt Geometry


Given a circle, TSW find the lengths of segments formed by lines that intersect circles and use the lengths of segments in circles to solve problems.

Objectives

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secant segmentexternal secant segmenttangent segment

Vocabulary

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In 1901, divers near the Greek island of Antikythera discovered several fragments of ancient items. Using the mathematics of circles, scientists were able to calculate the diameters of the complete disks.

The following theorem describes the relationship among the four segments that are formed when two chords intersect in the interior of a circle.

Holt Geometry


Holt Geometry


Example 1: Applying the Chord-Chord Product Theorem

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

EJ JF = GJ JH

10(7) = 14(x)

70 = 14x

5 = x

EF = 10 + 7 = 17

GH = 14 + 5 = 19

J

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Check It Out! Example 1

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

DE EC = AE EB

8(x) = 6(5)

8x = 30

x = 3.75

AB = 6 + 5 = 11

CD = 3.75 + 8 = 11.75

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Example 2: Art Application

The art department is contracted to construct a wooden moon for a play. One of the artists creates a sketch of what it needs to look like by drawing a chord and its perpendicular bisector. Find the diameter of the circle used to draw the outer edge of the moon.

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Example 2 Continued

8d = 145

8d – 64 = 81

8 (d – 8) = 9 9

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A secant segment is a segment of a secant with at least one endpoint on the circle. An external secant segment is a secant segment that lies in the exterior of the circle with one endpoint on the circle.

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Holt Geometry


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

Example 3: Applying the Secant-Secant Product Theorem

16(7) = (8 + x)8

112 = 64 + 8x

48 = 8x

6 = x

ED = 7 + 9 = 16

EG = 8 + 6 = 14

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

39(9) = (13 + z)13

351 = 169 + 13z

182 = 13z

14 = z

LG = 30 + 9 = 39

JG = 14 + 13 = 27

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A tangent segment is a segment of a tangent with one endpoint on the circle. AB and AC are tangent segments.

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Holt Geometry


Example 4: Applying the Secant-Tangent Product Theorem

Find the value of x.

The value of x must be 10 since it represents a length.

ML JL = KL2

20(5) = x2

100 = x2

±10 = x

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Find the value of y.

DE DF = DG2

7(7 + y) = 102

49 + 7y = 100

7y = 51

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Lesson Quiz: Part I

1. Find the value of d and the length of each chord.

d = 9

ZV = 17

WY = 18

2. Find the diameter of the plate.

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Lesson Quiz: Part II

x = 10

QP = 8

QR = 12

4. Find the value of a.

8

3. Find the value of x and the length of each secant segment.

holt geometry 11-6 segment relationships in circles 4 48 14 warm up solve for x. 1. 2. 3x = 12 2 3....

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