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5-Minute Check on Lesson 10-5 PowerPoint PPT Presentation


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Transparency 10-6. 5-Minute Check on Lesson 10-5. Determine whether each segment is tangent to the given circle . BC 2. QR Find x. Assume that the segments that appear to be tangents are tangents.

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5-Minute Check on Lesson 10-5

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5 minute check on lesson 10 5

Transparency 10-6

5-Minute Check on Lesson 10-5

  • Determine whether each segment is tangent to the given circle.

  • BC 2. QR

  • Find x. Assume that the segments that appear to be tangents are tangents.

  • 3. 4.

  • 5. What is the measure of PS?

Yes

No

x = 20√5

or 44.72

x = 12

Standardized Test Practice:

A

B

C

D

18

10

B

12

14

Click the mouse button or press the Space Bar to display the answers.


Lesson 10 6

Lesson 10-6

Secants, Tangents, and Angle Measures


Objectives

Objectives

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

  • Find measures of angles formed by lines intersecting outside a circle


Vocabulary

Vocabulary

  • Secant – a line that intersects a circle in exactly two points


Circles secants

y

x

Circles – Secants

Interior Angles formed by a Secant & a Tangentm3 = ½ (m Arc JMK)

m4 = ½ (m Arc JLK)

M

3

K

2

4

1

J

P

Center

Interior Angles formed by 2 Secantsm1 = ½ (m Arc MJ + m Arc LK)

m2 = ½ (m Arc MK + m Arc JL)

L


Circles external angles

Circles – External Angles

Two Secants

Secant & Tangent

Two Tangents

J

J

J

K

K

L

S

T

T

M

M

M

N

mJ = ½(m Arc TM – m Arc TK)

mJ = ½|m Arc TM – m Arc TK|

mJ = ½(m Arc TMS – m Arc TS)

mJ = ½|m Arc TMS – m Arc TS|

mJ = ½(m Arc MN – m Arc LK)

mJ = ½|m Arc MN – m Arc LK|


Example 6 1a

Find if and

Example 6-1a

Method 1


Example 6 1b

Example 6-1b

Method 2

Answer: 98


Example 6 1d

Find if and

Example 6-1d

Answer: 138


Example 6 2a

Find if and

Example 6-2a

Answer: 55


Example 6 2c

Find if and

Example 6-2c

Answer: 58


Example 6 3a

Example 6-3a

Find x.

Theorem 10.14

Multiply each side by 2.

Add x to each side.

Subtract 124 from each side.

Answer: 17


Example 6 3c

Example 6-3c

Find x.

Answer: 111


Example 6 4a

Example 6-4a

JEWELRY A jeweler wants to craft a pendant with the shape shown. Use the figure to determine the measure of the arc at the bottom of the pendant.

Let x represent the measure of the arc at the bottom of the pendant. Then the arc at the top of the circle will be 360 – x. The measure of the angle marked 40° is equal to 1/2 the difference of the measure of the two intercepted arcs.

Multiply each side by 2 and simplify.

Add 360 to each side.

Divide each side by 2.

Answer: 220


Example 6 4c

PARKS Two sides of a fence to be built around a circular garden in a park are shown. Use the figure to determine the measure of

Example 6-4c

Answer: 75


Example 6 5a

Example 6-5a

Find x.

Multiply each side by 2.

Add 40 to each side.

Divide each side by 6.

Answer: 25


Example 6 5c

Example 6-5c

Find x.

Answer: 9


Summary homework

Summary & Homework

  • Summary:

    • The measure of an angle formed by two secant lines is half the positive difference of its intercepted arcs

    • The measure of angle formed by a secant and tangent line is half its intercepted arc

  • Homework:

    • pg 564-566; 12-14, 18-20; 23-24, 26, 29, 34-36


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