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5-Minute Check on Lesson 10-5PowerPoint Presentation

5-Minute Check on Lesson 10-5

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5-Minute Check on Lesson 10-5

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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

Secants, Tangents, and Angle Measures

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

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

x

Circles – SecantsInterior Angles formed by a Secant & a Tangentm3 = ½ (m Arc JMK)

m4 = ½ (m Arc JLK)

M

3

K

2

4

1

J

P

Center

Interior Angles formed by 2 Secantsm1 = ½ (m Arc MJ + m Arc LK)

m2 = ½ (m Arc MK + m Arc JL)

L

Circles – External Angles

Two Secants

Secant & Tangent

Two Tangents

J

J

J

K

K

L

S

T

T

M

M

M

N

mJ = ½(m Arc TM – m Arc TK)

mJ = ½|m Arc TM – m Arc TK|

mJ = ½(m Arc TMS – m Arc TS)

mJ = ½|m Arc TMS – m Arc TS|

mJ = ½(m Arc MN – m Arc LK)

mJ = ½|m Arc MN – m Arc LK|

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 6-4a

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

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 6-4cAnswer: 75

Example 6-5a

Find x.

Multiply each side by 2.

Add 40 to each side.

Divide each side by 6.

Answer: 25

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