TOPIC VOCABULARY

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Check Your UnderstandingChoose the correct term to complete the sentence.

1. A(n) ? is a region bounded by an arc and the two radii to the arc’s endpoints.

2. A(n) ? is the measure of a central angle that intercepts an arc equal in length to a radius.

3. Coplanar circles that have the same center are called ? .

11-1 Circles and Arcs

ExercisesFind each measure.

4. m∠APD 5. m AC¬

6. mABD¬

7. m∠CPA

Find the length of each arc shown in red.

Leave your answer in terms of P.

8. 9.

10. 11.

AD

C

P

B608

4 in. 1108

1208

3 mm

10 m

5083 m

1208

ExampleA circle has a radius of 5 cm. What is the length of an arc

measuring 80°?

length of AB¬=mAB¬

360# 2pr Use the arc length formula.

=80

360# 2p(5) Substitute.

=209 p Simplify.

The length of the arc is 209 p cm.

Quick ReviewA circle is the set of all points

in a plane equidistant from a

point called the center.

The circumference of a circle

is C = pd or C = 2pr.

Arc length is a fraction of a

circle’s circumference. The

length of AB¬=mAB¬

360# 2pr.

B

O

C

ASemicircle

Minor arc

Diameter

Radius

Centralangle

ACB is amajor arc.

C

Topic 11 Review

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11-3 Areas of Circles and Sectors

ExercisesWhat is the area of each circle? Leave your answer in

terms of P.

19. 20.

Find the area of each shaded region. Round your answer

to the nearest tenth.

21. 22.

23. A circle has a radius of 20 cm. What is the area of the

smaller segment of the circle formed by a 60° arc?

Round to the nearest tenth.

12 in.

7 ft

6 cm

1208

8 cm

ExampleWhat is the area of the shaded region?

Area =m AB¬

360# pr2 Use the area

formula.

=120360

# p(4)2 Substitute.

=16p

3 Simplify.

The area of the shaded region is 16p3 ft2.

4 ftA

B1208

Quick ReviewThe area of a circle is A = pr2.

A sector of a circle is a region

bounded by two radii and their

intercepted arc. The area of

sector APB =m AB¬

360# pr2.

A segment of a circle is the part

bounded by an arc and the segment joining its endpoints.

Sectorof acircle

Segmentof acircle

BP

C

A

11-2 Radian Measure

ExercisesWrite each degree measure in radians and each radian

measure in degrees rounded to the nearest degree.

12. 60° 13. 45°

14. 180° 15. 2p radians

16. 5p6 radians 17.

3p4 radians

18. Use the circle to find the length of the indicated arc.

Round your answer to the nearest tenth.

3 5 ft

m

5p

ExampleWhat is the radian measure of an angle of 210°?

210° = 210° # p180°

radians =7p6 radians

Quick ReviewAn intercepted arc is the portion of the circle whose

endpoints are on the sides of an angle and whose remaining

points lie in the interior of the angle. A radian is the

measure of a central angle that intercepts an arc equal in

length to a radius of the circle.

480 Topic 11 Review

11-4 Circles in the Coordinate Plane

ExercisesWrite the standard equation of each circle below.

24.

25.

26. What is the standard equation of the circle with

radius 5 and center (-3, -4)?

27. What is the standard equation of the circle with

center (1, 4) that passes through (-2, 4)?

28. What are the center and radius of the circle with

equation (x - 7)2+ (y + 5)2

= 36?

y

x

O

23

2

y

x

O

2

2 4

4

ExampleWrite the standard equation of the circle shown.

y

x

O22 1

3

1

The center is (-1, 2). The radius is 2.

The equation of the circle is

(x - (-1))2+ (y - 2)2

= 22

or

(x + 1)2+ (y - 2)2

= 4.

Quick ReviewThe standard form of an equation of a circle with

center (h, k) and radius r is (x - h)2+ (y - k)2

= r2.

r

y

x

(h, k)

(x, y)

O

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