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A B C D. Refer to the figure. Find BC. 3. 5-Minute Check 4. A B C D. Refer to the figure. Find DE. 13. 5-Minute Check 5. A B C D. Find the length of the radius of the circle. 6.5 in. 5-Minute Check 6.

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5 minute check 4
A

B

C

D

Refer to the figure. Find BC.

3

5-Minute Check 4
5 minute check 5
A

B

C

D

Refer to the figure. Find DE.

13

5-Minute Check 5
5 minute check 6
A

B

C

D

Find the length of the radius of the circle.

6.5 in.

5-Minute Check 6
then now

Identify central angles, major arcs, minor arcs, and semicircles, and find their measures.

  • Find arc lengths.
Then/Now
vocabulary

central angle—an angle with a vertex in the center of the cricle

  • arc—a portion of a circle defined by two endpoints on the circle. An arc has the same measure of the central angle formed by its endpoints.
Vocabulary
example 11

The sum of the measures of

Find Measures of Central Angles

Substitution

Simplify.

Add 2 to each side.

Divide each side by 26.

Answer:x = 7

Example 1
example 12
A

B

C

D

Find the value of x.

9

Example 1
example 2

Answer:

Classify Arcs and Find Arc Measures

Example 2
example 22

Answer:

Classify Arcs and Find Arc Measures

Example 2
example 23

Answer:

Classify Arcs and Find Arc Measures

Example 2
example 3

Answer:

Find Arc Measures in Circle Graphs

mLPK = 0.21(360) Find 21% of 360.

= 75.6 Simplify.

Example 3
example 32

Answer:

Find Arc Measures in Circle Graphs

Sum of arc in circle is 360.

Substitution

Simplify.

Simplify.

Example 3
example 33
A

B

C

D

140.4

Example 3
example 34
A

B

C

D

273.6

Example 3
example 4

.

Use Arc Addition to Find Measures of Arcs

Example 4
example 41

Answer:

Use Arc Addition to Find Measures of Arcs

Arc Addition Postulate

= mLH + mHI

Substitution

= 58 + 32

= 90

Example 4
example 43

Answer:

Use Arc Addition to Find Measures of Arcs

Arc Addition Postulate

= mIJ + mJK

Substitution

= 90 + 58

= 148

Example 4
slide33

arc length—the distance between the endpoints along an arc measured in linear units. Since an arc is a portion of a circle, its length is a fraction of the circumference.

example 5

cm

Use a calculator.

Answer:

Find Arc Length

Arc Length Equation

Substitution

Example 5
example 51

Answer:

Find Arc Length

Arc Length Equation

Substitution

Use a calculator.

Example 5
example 52

Answer:

Find Arc Length

Arc Length Equation

Substitution

Use a calculator.

Example 5
example 53
A

B

C

D

3.77 cm

Example 5
example 54
A

B

C

D

38.61 cm

Example 5
example 55
A

B

C

D

32.99 cm

Example 5