1. Geometry B Bellwork
1) Find the length of the apothem of a regular hexagon given a side length of 18 cm.

2. 7-6 Circle and Arcs
Geometry

3. Finding circumference and arc length
The circumference of a circle is the distance around the circle.
For all circles, the ratio of the circumference to the diameter is the same. This ratio is known as  or pi.

4. Theorem 11.6: Circumference of a Circle
The circumference C of a circle is C = d or C = 2r,
where d is the diameter of the circle and r is the radius of the circle.

5. Ex. 1: Using circumference
Find (a) the circumference of a circle with radius 6 centimeters and (b) the radius of a circle with circumference 31 meters. Round decimal answers to two decimal places.

6. Solution: C = 2r = 2 •  • 6 = 12  37.70b. a.
C = 2r
= 2 •  • 6
= 12
 37.70
So, the circumference is about cm.
C = 2r
31 = 2r
31 = r
4.93  r
So, the radius is about 4.93 cm. 2

7. Arcs Arc- part of a circle Semicircle- half of the circle
Minor arc- smaller than a semicircle
Major arc- greater than a semicircle

8. Identify the following. Minor arcs Semicircles
Major arcs that contain point A D A P B C

9. E
Find the measures of
the arcs. DE EA EB
ADB
EBD D A
44°
78° P B C

10. Geometry B Bellwork 2)Find the measures of EB, BDE, ADB. E D A P B C
32°
82° P B C

11. Arc Length Theorem
The length of an arc of a circle is the product of the ratio, measure of the arc
360
and the circumference of a circle. r
Arc length of m AB AB =
• 2r
360°

12. More . . .
The length of a semicircle is half the circumference, and the length of a 90° arc is one quarter of the circumference.
½ • 2r r
¼ • 2r

13. Ex. 2: Finding Arc Lengths
Find the length of each arc. a. b. c.
50°
100°
50°

14. Ex. 2: Finding Arc Lengths
Find the length of each arc.
# of ° a.
• 2r
a. Arc length of AB =
360°
50°
a. Arc length of AB =
50°
360°
• 2(5)
 4.36 centimeters

15. Ex. 2: Finding Arc Lengths
Find the length of each arc.
# of ° b.
• 2r
b. Arc length of CD =
360°
50°
50°
• 2(7)
b. Arc length of CD =
360°
 6.11 centimeters

16. Ex. 2: Finding Arc Lengths
Find the length of each arc.
# of ° c.
• 2r
c. Arc length of EF =
360°
100°
100°
• 2(7)
c. Arc length of EF =
360°
 centimeters
In parts (a) and (b) in Example 2, note that the arcs have the same measure but different lengths because the circumferences of the circles are not equal.

17. Ex. 4: Comparing Circumferences
Tire Revolutions: Tires from two different automobiles are shown on the next slide. How many revolutions does each tire make while traveling 100 feet? Round decimal answers to one decimal place.

18. Ex. 4: Comparing Circumferences
Reminder: C = d or 2r.
Tire A has a diameter of (5.1), or 24.2 inches.
Its circumference is (24.2), or about inches.

19. Ex. 4: Comparing Circumferences
Reminder: C = d or 2r.
Tire B has a diameter of (5.25), or 25.5 inches.
Its circumference is (25.5), or about inches.

20. Ex. 4: Comparing Circumferences
Divide the distance traveled by the tire circumference to find the number of revolutions made. First, convert 100 feet to 1200 inches.
100 ft.
1200 in.
TIRE A:
TIRE B:
100 ft.
1200 in. = =
76.03 in.
76.03 in.
80.11 in.
80.11 in.
 15.8 revolutions
 15.0 revolutions

21. Ex. 5: Finding Arc Length
Track. The track shown has six lanes. Each lane is 1.25 meters wide. There is 180° arc at the end of each track. The radii for the arcs in the first two lanes are given.
Find the distance around Lane 1.
Find the distance around Lane 2.

22. Ex. 5: Finding Arc Length Find the distance around Lane 1.
The track is made up of two semicircles and two straight sections with length s. To find the total distance around each lane, find the sum of the lengths of each part. Round decimal answers to one decimal place.

23. Ex. 5: Lane 1 Ex. 5: Lane 2 Distance = 2s + 2r1
= 2(108.9) + 2(29.00)
 meters
Distance = 2s + 2r2
= 2(108.9) + 2(30.25)
 meters
Ex. 5: Lane 2