chapter 10.6 and 10.7 secants, tangents, and angle measures and special segments in a circle

CHAPTER 1

0.6 A

ND 10.7

SECANTS

, TANGENTS

, AND A

NGLE

MEASURES AND

SPECIA

L SEGMEN

TS IN

A C

IRCLE

A secant is a line that intersects a circle in exactly two points.

SECANT

CONCEPT

Use Intersecting Chords or Secants

A. Find x.

Answer: x = 82

Use Intersecting Chords or Secants

B. Find x.

C. Find x.

Use Intersecting Chords or Secants

Answer: x = 95

A. 92

B. 95

C. 97

D. 102

B. Find x.

A. 96

B. 99

C. 101

D. 104

C. Find x.

A. 92

B. 95

C. 98

D. 104

A. Find x.

CONCEPT

Use Intersecting Secants and Tangents

A. Find mQPS.

Answer: mQPS = 125

B.

Use Intersecting Secants and Tangents

Answer:

A. 98

B. 108

C. 112.5

D. 118.5

A. Find mFGI.

A. 99

B. 148.5

C. 162

D. 198

B.

CONCEPT

Use Tangents and Secants that Intersect Outside a Circle

A.

Use Tangents and Secants that Intersect Outside a Circle

B.

A. 23

B. 26

C. 29

D. 32

A.

A. 194

B. 202

C. 210

D. 230

B.

EXAMPLE 4Apply Properties of Intersecting Secants

CONCEPT

CONCEPT

When two chords intersect inside a circle, each chord is divided into two segments, called chord segments.

Use the Intersection of Two Chords

A. Find x.

EXAMPLE 1Use the Intersection of Two Chords

B. Find x.

A. 12

B. 14

C. 16

D. 18

A. Find x.

EXAMPLE 1

A. 2

B. 4

C. 6

D. 8

B. Find x.

CONCEPT

Use the Intersection of Two Secants

Find x.

A. 28.125

B. 50

C. 26

D. 28

Find x. Needs to be changed!

CONCEPT

EXAMPLE 4Use the Intersection of a Secant and a Tangent

LM is tangent to the circle. Find x. Round to the nearest tenth.

A. 22.36

B. 25

C. 28

D. 30

Find x. Assume that segments that appear to be tangent are tangent.