Topic 11 Review - Birdville Schools · Topic 11 Review PearsonTEXAS.com 479. 11-3 Areas of Circles...
Transcript of Topic 11 Review - Birdville Schools · Topic 11 Review PearsonTEXAS.com 479. 11-3 Areas of Circles...
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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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