7.7 - Unit 7 Test Review (Circles)

Unit 7 Review

• Circle Equations

• Angles & Lines in Circles

• Arc Length & Sector Area

Standard Form

Match

Match each Circle equation to its correct center and radius.

• $$\left(x-3\right)^2+\left(y+3\right)^2=9$$

• $$\left(x+3\right)^2+\left(y-3\right)^2=9$$

• $$\left(x+3\right)^2+\left(y-3\right)^2=3$$

• $$x^2+\left(y+3\right)^2=9$$

• $$\left(x-3\right)^2+\left(y-3\right)^2=3$$

Center @ (3,-3); radius = 3

Center @ (-3,3); radius = 9

Center @ (-3,3); radius =

Center @ (0,-3); radius=3

Center @ (3,3); radius=

• Center @ (3,-3); radius = 3

• Center @ (-3,3); radius = 9

• Center @ (-3,3); radius = $$\sqrt[]{3}$$

• Center @ (0,-3); radius=3

• Center @ (3,3); radius= $$\sqrt[]{3}$$

Multiple Choice

Which graph corresponds to 
(x)²+ (y-6)²=9

• A

• B

• C

• D

Multiple Choice

Which graph corresponds to

(x-4)²+ (y+4)²=25

• A

• B

• C

• D

Multiple Choice

What is the equation of the circle?

• (x+1)² + (y +1)² = 3

• (x+1)² + (y -1)² = 3

• (x+1)² + (y +1)² = 9

• (x-1)² + (y -1)² = 9

Multiple Choice

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

• (x - 5)² + (y + 2)² = 36

• (x + 5)² + (y - 2)² = 6

• (x + 5)² + (y - 2)² = 36

• (x + 5)² + (y - 2)² = 144

Multiple Choice

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9

• x² + (y -7)² = 9

• (x - 7)² + y² = 3

• x² + (y -7)² = 3

How could you determine if a point is on a circle?

Poll

Which of the following points are on the circle $$\left(x-5\right)^2+\left(y+3\right)^2=18$$ ?

• (5, -3)

• (2, 0)

• (8, -6)

• (7, 1)

• (1, -5)

• (5, -3)

• (2, 0)

• (8, -6)

• (7, 1)

• (1, -5)

​

1.) Isolate the constant

2.) Group x & y terms together

3.) Complete the square for x & y (divide 'b' by 2, square that number)

4.) Factor

​

Converting General Form to Standard Form

Multiple Choice

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

• (x+2)² + (y+3)² = 49

• (x+2)² + (y+3)² = 13

• (x-2)² + (y-3)² = 49

• (x-2)² + (y-3)² = 13

Multiple Choice

Find the center and radius of the circle: x² + y² + 14x - 2y + 1 = 0.

• center = (-7, 2) radius = 3

• center = (-7, 1) radius = 7

• center = (-4, 1) radius = 7

• center = (-4, 2) radius = 3

Multiple Choice

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

• (x+2)² + (y+3)² = 49

• (x+2)² + (y+3)² = 13

• (x-2)² + (y-3)² = 49

• (x-2)² + (y-3)² = 13

Multiple Choice

What is the center for the circle with this equation x² + y² + 4x + 6y - 36 = 0?

• (-2, 5)

• (2, 7)

• (-2, -7)

• (-2, -3)

Multiple Choice

Determine the center and radius: x² + y² - 10x + 8y - 8 = 0

• C = (5,-4) r = 7

• C = (-5,4) r = 7

• C = (-4,5) r = 49

• C = (5,-4) r = 49

Multiple Choice

Determine the center and radius: x² + y² + 14x - 2y + 1 = 0

• center= (-7,2) radius= 3

• center= (-7,1) radius= 7

• center= (-4,1) radius= 5

Multiple Choice

Determine the equation of the circle in standard form: x² + y² + 6x - 12y + 20 = 0

• (x-3)² + (y+6)² = 25

• (x+3)² + (y-6)² = 25

• (x-3)² + (y+6)² = 45

• (x+3)² + (y-6)² = 5

Lines & Angles in Circles

Match

Match each angle to the correct theorem you would use to find a missing angle or arc measure.

Opposite angles are supplementary (180)

• $$\angle=\frac{1}{2}\left(Arc\right)$$

• $$\angle=Arc$$

• $$\angle=\frac{1}{2}\left(Arc+Arc\right)$$

• $$\angle=\frac{1}{2}\left(Arc-Arc\right)$$

• Opposite angles are supplementary (180)

Multiple Choice

What is the measure of arc AB?

• 38

• 142

• 180

• 72

Multiple Choice

What is the measure of arc KL?

• 108

• 27

• 54

• 112

Multiple Choice

What is the measure of angle DEF?

• 72

• 288

• 144

• 75

Multiple Choice

What is the measure of angle HKI?

• 32

• 73

• 52.5

• 75

Multiple Choice

What is the measure of arc GF?

• 168

• 114

• 138

• 21

Multiple Choice

What is the measure of arc AD?

• 137

• 240

• 111.5

• 343

Multiple Choice

Find x.

• 29⁰

• 33⁰

• 41.5⁰

• 50⁰

Multiple Choice

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

• 68°

• 49°

• 47°

• 72°

Multiple Choice

Find the measure of the arc or angle indicated. Assume that lines which appear tangent are tangent.

• 132°

• 65°

• 130°

• 95°

Multiple Choice

Find a and b.

• a=74 degrees b=93 degrees

• a=93 degrees b=74 degrees

• a=87 degrees b=106 degrees

• a=106 degrees b=87 degrees

Multiple Choice

Solve for x and y.

• x=85⁰  y = 150⁰

• x = 85⁰  y = 50⁰

• x = 95⁰   y = 150⁰

• x = 95⁰   y = 50⁰

Match

Match each diagram to the theorem you would use to find a missing length of a segment.

(shortens down)

Both lines are congruent

Pythagorean Theorem

• $$piece\times piece=piece\times piece$$

• $$outside\times whole=outside\times whole$$

• $$outside\times whole=outside\times whole$$ (shortens down)

• Both lines are congruent

• Pythagorean Theorem $$a^2+b^2=c^2$$

Multiple Choice

Solve for x

• 9

• 6

• 14

• 4

Multiple Choice

Solve for NL

• 10

• 6

• 22

• 15

Multiple Choice

Solve for x.

• x = 12

• x = 24

• x = 2

• x = 53

Multiple Choice

Find the radius r

• 2

• 3

• 4

• 5

Multiple Choice

Solve for x.

• x = 32

• x = 23

• x = 30

• x = 18

Multiple Choice

Solve for x.

• x = 15

• x = 3

• x = 16

• x = 2/3

Multiple Choice

Solve for x

• 2

• 3

• 4

• 5

Multiple Choice

Solve for x.

• x = 21

• x = 22

• x = 4

• x = 42

Multiple Choice

Solve fro x.

• x = 7

• x = 12

• x = 8

• x = 13

Multiple Choice

Solve for x.

• x = 9

• x = 0

• x = 10

• x = 6

Sector Area & Arc Length

Sector Area & Arc Length - Big Ideas

Multiple Choice

Find the area of each sector.

• 52.4 in²

• 18,864 in²

• 60 in2

• 10.47 in

Multiple Choice

Alison is jogging on a circular track that has a radius of 140 feet.  She runs along the track from point R to point N, a distance of 230 feet. Find the radians measure of the arc she jogged

• $$\frac{23}{14}$$

• $$\frac{14}{23}$$

• 94

• $$\frac{115}{\pi}$$

Multiple Choice

Find the arc length.  Leave your answer in terms of π.

• 7/4π

• 7/2π

• 1/8π

• 45π

Multiple Choice

Find the arc length of arc AB.

• 12.57 units

• 75.40 units

• 24 units

• 125.66 units

Multiple Choice

Find the area of the shaded sector of circle O.  Express answer to the nearest tenth of a square inch.

• 9.2 sq. in.

• 10.5 sq. in.

• 31.4 sq. in.

• 38.2 sq. in.

Multiple Choice

Find the area of the shaded region bounded by two concentric circles (see diagram)

• 125.7 cm²

• 40 cm²

• 103.7 cm²

• 33 cm²

Multiple Choice

If Pacman's mouth, when open, is 70° and the radius of his mouth is 8mm, what is the area of the rest of Pacman's body?

• 161.97 mm²

• What's Pacman?

• 39.1 mm²

• 9.77 mm²

Multiple Choice

Given the measure of the angle AOB is 

$$\frac{2\pi}{5}$$ radians and the radius of the circle is 5 cm, what is the EXACT length of the arc AB?

• $$\frac{2}{5}\pi$$   cm

• $$\frac{\pi}{2}$$   cm

• $$2\pi$$   cm

• $$5\pi$$