Circles

Question 0

What is a Circumference?

Answer 0

The edge of a circle

Question 1

What is a Radius?

Answer 1

A line from the center of a circle to its edge

Question 2

What is a Diameter?

Answer 2

A line splitting the circle through its center

Question 3

What is a Tangent?

Answer 3

A line that touches the edge of a circle but doesn’t enter it

Question 4

What is a Points of Tangency?

Answer 4

The point where a radius touches a tangent. This always creates right angles

Question 5

What is a Secant?

Answer 5

A line that cuts through a circle (touching it in two places)

Question 6

What is a Chord?

Answer 6

A line that starts and ends at the edge of a circle. The longest chord will be the diameter

Question 7

What is a Sector?

Answer 7

Pie shaped pieces of a circle

Question 8

What is a Minor Arc?

Answer 8

Less than half a circle

Question 9

What is a Major Arc?

Answer 9

More than half a circle

Question 10

What is a Semicircle?

Answer 10

Half a circle

Question 11

What is the area of a circle?

Answer 11

πr²

Question 12

How do you find the circumference of a circle?

Answer 12

2πr

πd

Question 13

How do you find the area of a sector?

Answer 13

θ
—— (πr²)
360º

θ = Inner Angle

Question 14

How do you find the arc length of a sector?

Answer 14

θ
—— (2πr)
360º

θ = Inner Angle

Question 15

How do you find the perimeter of a sector?

Answer 15

AL + 2r

AL = Arc Length

Question 16

If the area of ΔAOB is 25, what is the area of circle O?

Answer 16

ΔAOB: ½(r)(r) or ½r². So 50 = r²

O: 50π.

(Area of a circle = πr²)

Question 17

If the OA = 8, what is the area of the shaded region BAYB?

Answer 17

ΔAOB: ½(8)(8) = ½(64) = 32

O: π(8²) = 64π

Sector BYAOB: ¼(64π) = 16π

Shaded Region: 16π - 32 = 16(π - 2)

Question 18

If CD = 10, what is the perimeter of sector DOCXD?

Answer 18

ΔDOC is equilateral. All sides will equal 10.

Arc Length DXC: 36/360(2π)(10) = 1/6(20π) = 1/3(10π) =
= 10π/3

Perimeter: 10π/3 + 2(10) = 10π/3 + 20

Question 19

If OC = 2, what is the area of the shaded portion DCXD?

Answer 19

ΔCOD: 2²√3/4 = 4√3/4 = √3

Sector DCXD: 60/360(π)(2²) = 1/6(4π) = 1/3(2π) = 2π/3

Shaded Area: 2π/3 - √3 or…..

2π/ - 3√3
————-
3

Question 20

If the area of ΔCOD is 25√3, what is the perimeter of semicircle EOBDXCE?

Answer 20

25√3 = x²√3/4 || 100√3 = x²√3 || 100 = x² || 10 = x

Arc BDXCE: 180/360(2π)(10) = ½(2π)(10) = 10π

Semicircle EOBDXCE Perimeter: 10π + 2(10) =
= 10π + 20 -or- 10(x + 2)

Question 21

What is the perimeter of this figure?

Answer 21

Δ: 8² + 6² = x² || 64 + 36 = x² || 100 = x² || 10 = x

AL: 90/360(2π)(10) = 1/4(2π)(10) = 1/2π(10) = 5π

Figure: 8 + 6 + 5π = 14 + 5π

Question 22

If AB = 10, what is the the area of the shaded portion?

Answer 22

❏ = (10)(10) = 100

❍ = π(5²) = 25π

Shade: 100 - 25π

Question 23

If OC bisects AB, AB = 16, and OC = 6, what is the area of the circle?

Answer 23

AC = 8

AO = 10

❍: π(10²) = 100π