Geometry b chapter 10
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Geometry B Chapter 10. Segment Relationships in Circles. Objectives. Find the lengths of segments formed by lines that intersect circles. Use the lengths of segments in circles to solve problems. Warm Up Solve for x . 1. 2. 3 x = 12 2 3. BC and DC are tangent

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Geometry B Chapter 10

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Geometry b chapter 10

Geometry BChapter 10

Segment Relationships in Circles


Geometry b chapter 10

Objectives

Find the lengths of segments formed by lines that intersect circles.

Use the lengths of segments in circles to solve problems.


Geometry b chapter 10

Warm Up

Solve for x.

1.

2. 3x = 122

3. BC and DC are tangent

to A. Find BC.

4

48

14


Geometry b chapter 10

Vocabulary

secant segment

external secant segment

tangent segment


Geometry b chapter 10

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.


Geometry b chapter 10

J

Example 1: Applying the Chord-Chord Product Theorem

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

10(7)= 14(x)

70 = 14x

5 = x

EF = 10 + 7 = 17

GH = 14 + 5 = 19


Geometry b chapter 10

In Your Notes! Example 1

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

8(x) = 6(5)

8x = 30

x = 3.75

AB = 6 + 5 = 11

CD = 3.75 + 8 = 11.75


Geometry b chapter 10

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.


Geometry b chapter 10

Example 2 Continued

8(d – 8) = 9  9

8d – 64 = 81

8d = 145


Geometry b chapter 10

6 in.

In Your Notes! Example 2

What if…? Suppose the length of chord AB that the archeologists drew was 12 in. In this case how much longer is the disk’s diameter compared to the disk on p. 793?

6(6) = 3(QR)

12 = QR

12 + 3 = 15 = PR


Geometry b chapter 10

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


Geometry b chapter 10

Example 3: Applying the Secant-Secant Product Theorem

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

112 = 64 + 8x

48 = 8x

6 = x

ED = 7 + 9 = 16

EG = 8 + 6 = 14


Geometry b chapter 10

In Your Notes! Example 3

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

351 = 169 + 13z

182 = 13z

14 = z

LG = 30 + 9 = 39

JG = 14 + 13 = 27


Geometry b chapter 10

A tangent segmentis a segment of a tangent with one endpoint on the circle. ABand ACare tangent segments.


Geometry b chapter 10

Example 4: Applying the Secant-Tangent Product Theorem

Find the value of x.

ML JL = KL2

20(5) = x2

100 = x2

±10 = x

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


Geometry b chapter 10

In Your Notes! Example 4

Find the value of y.

DE DF = DG2

7(7 + y) = 102

49 + 7y = 100

7y = 51


Geometry b chapter 10

Lesson Quiz: Part I

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

2. Find the diameter of the plate.


Geometry b chapter 10

Lesson Quiz: Part II

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

4. Find the value of a.


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