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Geometry > Geometry (Circles Part. 2) > Flashcards

Geometry (Circles Part. 2) Flashcards

1
Q

Arc Length

(Definition)

A

A portion of the circumference of the circle.

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2
Q

Explain how you get the Arc Length (Degrees) Equation

A
  1. You need the central angle that subtends the arc length.
  2. From there, you can divide that angle (In degrees) by (360°) to receive the ratio of the Arc Length in comparison to the entire Circumference.
  3. Then, you multiply the ratio of the Arc Length and the Circumference to receive the total Arc Length

* From that information, you can create and manipulate the equation to determine the Arc Measure or Circumference of a Circle (In degrees)

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3
Q

Arc Length

(Degrees Equation)

A

Arc Length = (Central Angle/ 360°) Circumference

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4
Q

In the figure below, line (DB) and (AC) are diameters of circle P. The length of line (PB) is 8 units.

What is the length of curve (DC)?

A

(16/3)π

or

16.76

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5
Q

In the figure below, line (BC) is a diameter of circle P. The length of line (BP) is 3 Units.

What is the length of curve (ACD)?

A

(65/12)π

or

17.02

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6
Q

In the figure below, angle (APB) ≈ angle (BPC). The length of line (PB) is 4 units.

What is the length of curve (BC)?

A

(104/45)π

or

7.26

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7
Q

Central angle

(Equations)

A

Central Angle = (Arc length/ Circumference) (360°)

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8
Q

In the figure below, the radius of circle p is 10 units. Arc (ABC) has a length of 16π.

What is the measure of Arc (AC), in degrees?

A

72°

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9
Q

In the figure below, the radius of circle P is 18 units. The length of Arc (BA) is 14π.

What is the measure of Arc (BC) in degrees?

A

64°

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10
Q

Circumference (From Arc Length and Central Angle)

(Equations)

A

Circumference = (360° / Central Angle) (Arc Length)

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11
Q

Degree

(Definition)

A

A unit of measurement of angles, equal to 1/360 of the circumference of a circle.

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12
Q

Radian

(Definition)

A

Describes the plane angle subtended by a circular arc as the length of the arc divided by the radius of the arc.

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13
Q

Explain how you get the Equation to convert (Radians to Degrees)

A

360 (Degrees) = Circumference

2π (Radians) = Circumference

360 (Degrees) = 2π (Radians)

180 (Degrees) = π (Radians)

180/π (Degrees) = (Radians)

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14
Q

Radian to degrees

(Equation)

A

1 Radian = (180/π) Degrees

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15
Q

Convert the angle Ø = (23π/20) radians to degrees.

A

207°

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16
Q

Convert the angle Ø = (8π/9) radians to degrees.

A

160°

17
Q

Convert the angle Ø = (17π/18) radians to degrees.

A

170°

18
Q

Degree to Radians

(Equation)

A

1 Degree = (π/180) Radians

19
Q

Convert the angle Ø = 290° to radians.

A

29π/18 Radians

20
Q

Convert the angle Ø = 260° to radians.

A

13π/9 Radians

21
Q

Convert the angle Ø = 100° to radians.

A

5π/9 Radians

22
Q

Explain how you get the Arc Length Equation in Radians.

A
  1. We established the Arc Length (Degree Equation) to be

Arc Length = (Central Angle/ 360°) (Circumference)

  1. We can substitue (360-Degrees) with (2π-Radians).
  2. We also substitute the (Circumference) with (2πr)
  3. The new equation we get is

Arc Length = (Central angle/ 2π) (2πr)

  1. Then we simplify (Central angle x 2πr) / (2π) to get

Arc Length = Central Angle x Radius

23
Q

Arc Length

(Radian Equation)

A

Arc Length = Arc Measure (Radians) x Radius

24
Q

What is the exact length of Curve (BCA)?

A

85π/2

25
Q

What is the exact length of Curve (DAC) on Circle P?

A

5π

26
Q

What is the exact length of Curve (CD)?

A

35π/18

27
Q

Arc Measure

(Radian Equation)

A

Arc Measure = Arc Length/ Radius

28
Q

What is the arc measure of Curve (AB), in radians?

A

17π/30

29
Q

What is the arc measure of Curve (CD), in radians?

A

π/5

30
Q

What is the arc measure of Ø in radians?

A

7π/6

31
Q

Area of a circle

(Equation)

A

Area of a circle = πr2

32
Q

What is the area of the Sector?

A

27π

33
Q

What is the area of the Sector?

A

45π/4

34
Q

What is the area of the Circle?

A

9π

35
Q

What is the area of the Sector?

A

45π/4

Geometry (7 decks)

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