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Geometry > 2.B Circles > Flashcards

2.B Circles Flashcards

1
Q

What is a circle?

A

A figure that is connected by one line around a center point with all points on the line being the same distance away as the center point.

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2
Q

What is a tangent line on a circle?

A

A line that only intersects a circle once.

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3
Q

What is a chord on a circle?

A

A line segment inside the circle that connects two points on the circle.

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4
Q

What is the diameter of the circle?

A

Basically a chord drawn down the middle of the circle splitting it into halves.

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5
Q

What is the radius of a circle?

A

A radius of a circle is the distance from any point on the circle to it center.
A radius can also be measured by dividing the diameter in half.

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6
Q

What is a secant?

A

A line that intersects a circle at two points.

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7
Q

What are the 3 different types of circles angles?

A
  1. Central Angle
  2. Inscribed Angle
  3. Circumscribed Angle
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8
Q

What are the different types of arcs?

A
  1. Intercepted Arc
  2. Minor Arcs
  3. Major Arcs
  4. Semicircles
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9
Q

What are the two types of Circle Similarity?

A
  1. Concentric Circles
  2. Congruent Circles
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10
Q

What are concentric circles?

A

Circles that have the same center, but have a different radii.

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11
Q

What is true about the radius of a circle and its corresponding tangent line?

A

The radius of a circle and and the tangent line that goes through its corresponding point are always perpendicular.

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12
Q

What is the relationship between an inscribed angle and it’s corresponding central angle.

A

An inscribed angle given will be half its corresponding central angle.

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13
Q

If the measure of the inscribed angle is 90° then what is the central angle?

A

180°

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14
Q

What is the relationship between central angles and their corresponding circumscribed angle?

A

Because tangent lines equal 90° and the angles all create a kite, the central angle and the circumscribed angle will be supplementary to each other. (Equal 180°)

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15
Q

What is true about chords and the diameter of the circle.

A

The diameter will bisect the chord and create a 90° angle.

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16
Q

What is true about angles formed by intersecting chords?

A

The angle measure will be equal to half the sum of both intersecting angles.

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17
Q

What is the equation you should use for two intersecting chord lengths?

A

Use (AP)(BP) = (CP)(PD)
- The measures of these angles will be equal to the sum of the corresponding opposite arcs divided by 2.

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18
Q

When given two tangents and asked for the angle between them what equation do you use?

A

The measure of the angle between two tangent lines is equal to the bigger arc minus the smaller arc and then divided by 2.
Equation: θ = 1/2(Big Arc - Small Arc)

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19
Q

What is true about two tangent lines forming a circumscribed angle?

A

Their lengths are the same

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20
Q

What equation should you use when given two secants and asked for the circumscribed angle they form?

A

Use θ = 1/2(Big Arc - Small Arc)
- The lengths of this angle equal to each other like this: (small angle segment length)(whole segment length) = (smol)(whole)

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21
Q

When a secant and a tangent form an angle on the circle the measure of the angle will be equal to…

A

The measure of this angle will be half the arc it is opening toward.

22
Q

When a secant and a tangent form an angle outside the circle than what can be said about the angle measurement?

A

The angle’s measurement will be equal to the difference of the opposite big arc and the corresponding littler arc divided by 2.
- The lengths of these segments can be found using this equation: (tangent)2 = (tiny secant segment)(whole secant length)

23
Q

How do you find the circumference of a circle?

A

Circumference = 2πr or π × d

24
Q

How do you find the total area of a circle?

A

Area = πr2

25
Q

How do you find the arc length of an angle?

A

length of arc/2πr = θ°/360°
or
θ°/360° times 2πr

26
Q

How do you find the arc angle?

A

Its the same as the central angle.

27
Q

How do you find the Radian Measure?
(Find the radius using the central angle)

A

θ = central angle/180° × π

28
Q

How do you find the area of a sector?
(Use proportions to find area)

A

sector area/πr2 (total area) = θ°/360°
or
Sector area = θ°/360° × πr2

29
Q

How do you solve for the Central Angle in Radians?

A

arc length/radius

30
Q

How can you find an Inscribed Circle in a triangle?

A
  1. Find two angle bisectors and label intersection (center)
  2. Using that point measure the distance to one side (radius)
  3. Draw circle
31
Q

How can you find a Circumscribed Circle?

A
  1. Find the 2 perpendicular bisectors of the circle
    - if the triangle is acute, the point of intersection will be inside the triangle
    - if the triangle is right then the point will lie on the triangle.
    - if the triangle is obtuse it will be outside the triangle.
  2. Using the point of intersection as the center of the circle measure the distance from center to any vertex to get radius.
  3. Draw Circle
32
Q

What are the properties of an Inscribed Quadrilateral?

A
  • opposite sides are supplementary
  • the only type of specific quadrilateral that is possible inside a circle are rectangles.
33
Q

What is the Standard Form of a Circle when the origin is (0,0)?

A

x2 + y2 = r2

34
Q

What is the Standard Form of a Circle when the origin is any given point?

A

(x - h2) + (y - k)2 = r2

35
Q

What is the General Form of a Circle?

A

Ax2 + By2 + Cx + Dy + E (ick)

36
Q

What does (h,k) represent in a circle?

A

They represent the center coordinates while (x,y) represents a point on the circle.

37
Q

When given two coordinates as the diameter how should you find the center?

A

Use the midpoint formula and then use the distance formula to figure out the radius and complete standard form equations.

38
Q

What is the standard form of Vertical Parabolas?

A

y = a(x - h)2 + k

39
Q

How do you find the focus of Vertical Parabolas

A

Focus = (h, k + p)

40
Q

How do you find the Directrix of a Vertical Parabola?

A

Directrix: y = k - p

41
Q

What does the value of “p” represent?

A

“p” represents the distance from the vertex to the focus

42
Q

What is the mini equation for “p”?

A

p = 1/4a

43
Q

What does the value of “a” determine?

A

The value “a” determines how wide or narrow a graph is as well as if it opens up or down or left or right.
- Vertical Parabolas: (a > 0) opens up, (a < 0) opens down.
- Horizontal Parabolas: (a > 0) opens right, (a < 0) opens left

44
Q

What is the mini equation for “a”?

A

a = 1/4p

45
Q

What is the standard form of Horizontal Parabolas?

A

x = a(y - k)2 + h (switch!)

46
Q

How do you find the focus of Horizontal Parabolas?

A

Focus = (h + p, k)

47
Q

How do you find the directrix of a Horizontal Parabola?

A

Directrix: x = h - p

48
Q

Every point on a Parabola is _________ from the focus and its directrix

A

equidistant

49
Q

What does (h,k) represent in a Parabola?

A

The variables (h,k) represent the coordinates of the vertex of the Parabola.

50
Q

Do you have this exam in the bag

A

Yes ma’am 🫡

Geometry (10 decks)

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