10-6 Secants, Tangents, and Angle Measures

You found measures of segments formed by tangents to a circle.

• Find measures of angles formed by lines intersecting on or inside a circle.

• Find measures of angles formed by lines intersecting outside the circle.

One line, One circle, Same plane….

The line intersects the circle in two points.It is a secant line.

p. 741

Use Intersecting Chords or SecantsA. Find x.

Answer: x = 82

Theorem 10.12

Substitution

Simplify.

Use Intersecting Chords or SecantsB. Find x.

Theorem 10.12

Substitution

Simplify.

Step 1 Find mVZW.

Step 2 Find mWZX.mWZX = 180 – mVZW Definition of

supplementary angles

x = 180 – 79 Substitution

x = 101 Simplify.

Answer: x = 101

C. Find x.

Theorem 10.12

Substitution

Multiply each side by 2.

Subtract 25 from each side.

Answer: x = 95

A. 92

B. 95

C. 98

D. 104

A. Find x.

A. 96

B. 99

C. 101

D. 104

C. Find x.

12

(30+𝑥 )=67

15+ 12 𝑥=6712 𝑥=52

𝑥=104

p. 742

A. Find mQPS.

Theorem 10.13

Substitute and simplify.

Answer: mQPS = 125

B.

Theorem 10.13

Use Intersecting Secants and Tangents

Substitution

Multiply each side by 2.

Answer:

A. 98

B. 108

C. 112.5

D. 118.5

A. Find mFGI.

225 ° ÷2=112.5

A. 99

B. 148.5

C. 162

D. 198

B.

180−99=8181×2=162

p. 743

Use Tangents and Secants that Intersect Outside a Circle

A.

Theorem 10.14

Substitution

Multiply each side by 2.

Subtract 141 from each side.

Multiply each side by –1.

Use Tangents and Secants that Intersect Outside a CircleB.

Theorem 10.14

Substitution

Multiply each side by 2.

Add 140 to each side.

A. 23

B. 26

C. 29

D. 32

A.

56=12(135−𝑚𝑄𝑆 )

112=135−m𝑄𝑆−23=−𝑄𝑆𝑄𝑆=23

A. 194

B. 202

C. 210

D. 230

B.

50=12(𝑚𝐹𝐼𝐻−130 )

100=(𝑚𝐹𝐼𝐻−130 )

230=𝑚𝐹𝐼𝐻

p. 745

10-6 Assignment

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