circle facts pt.1 Flashcards

1
Q

a line segment from the center of a circle to ANY point on the circle

A

radius

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2
Q

line segment whose endpoints are both points on the circle

A

chord (yay)

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3
Q

a chord passing through the CENTER of the circle

A

diameter

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4
Q

a line intersecting the circle in exactly one point (point of tangency), does not touch circle except for this one particular spot

A

tangent

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5
Q

a line intersecting or passing through the circle in 2 different distinct points

A

secant

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6
Q

an angle whose vertex is the center (!) of the circle and whose rays are radii of the circle

A

central angle

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7
Q

a part of the circle; can be intercepted by angles, chords, secants, and tangents

A

arc

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8
Q

an angle whose vertex is on the circle and whose rays are chords (!) of the circle

A

inscribed angle

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9
Q

an arc forming half a circle

A

semicircle!

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10
Q

an arc measuring LESS than a semicircle (2 LETTERS)

A

minor arc

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11
Q

an arc measuring MORE than a semicircle (3 LETTERS)

A

major arc

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12
Q

circles with the same center but not necessarily the same radius

A

concentric circles

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13
Q

where can a circle be inscribed?

A

a polygon with each side of the polygon tangent to the circle

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14
Q

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

A

center radius form

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15
Q

ax2 + bx2 + cx + dy + e = 0

A

standard form

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16
Q

Circle Fact 1

A

A central angle is = to its intercepted arc (in degrees)

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17
Q

Circle Fact 2

A

An inscribed angle is equal to half its intercepted arc in degrees

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18
Q

when given a question listing 2 coordinates on a plane asking for the area of a sector

A

match up right triangle, find value of x via inverse of tangent and proceed with area sector formula

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19
Q

Limit argument (dissection)

A

the smaller the angle values are of each sector the circle is divided into, the more it resembles a parallelogram

20
Q

Semi circle SA

A

1/2 pi radius squared

21
Q

Quarter Circle SA

A

1/4 pi radius squared

22
Q

any sector SA

A

x/360 pi radius squared

23
Q

Arc length

A

n/360 pi diameter or n/360 2 pi radius

24
Q

construction for equilateral triangle

A

1) diameter & plot
2) draw vertical curve after using compass to measure radius
3) connect plots

25
construction for hexagon
1) diameter & plot 2) draw vertical curve after using compass to measure radius 3) connect plots 4) do for both sides
26
construction of a square
1) diameter and plot 2) perp bisect 3) connect plots
27
construction of an octagon
1) diameter and plot 2) perp bisect (4x) 4) connect plots
28
radian measure
radius to degrees - 180 over pi degrees to radius- pi over 180
29
(x-h)2 + (y-k)2 = r2
circle radius form, convert to standard form via perfect square
30
ax2 + by2 +cx +dy + e = 0
standard form, combine like terms
31
circumference formula
pi(d) or 2pi(r)
32
limit argument for area & circumference
the smaller the angle measure at which each sector is dissected, the more it resembles a parallelogram 1/2 (2 pi r Radius is height Base x2 = circumference 1/2 (2pir) (r) base = 1/2 (2 pi r), simplifies to pi r plus the radius is pi r2, which is the area of a rectangle
33
Circle Fact 3
An angle formed by a chord and a tangent is equal to half its intercepted arc
34
Circle Fact 4
An angle formed by two chords/two lines intersecting INSIDE a circle is equal to half the SUM of its intercepted arcs
35
Circle Fact 5
An angle formed by any two lines intersecting OUTSIDE of a circle is equal to half the DIFFERENCE of the intercepted arcs
36
Circle Fact 6
If a quadrilateral is inscribed in a circle, the opposite angles are supplementary
37
Circle Fact 7
A radius drawn to the point of tangency is perpendicular to the tangent
38
Circle Fact 8
A radius or diameter perpendicular to a chord bisects the chord and its arcs (and a radius or diameter that bisects a chord is perpendicular to that chord)
39
CIrcle Fact 9
Equal chords intercept equal arcs
40
Circle Fact 10
Parallel chords create congruent arcs
41
Circle Fact 11
Chords equidistant from the center of a circle are congruent
42
Circle Fact 12
Two tangents drawn from the same external point to a circle are congruent
43
Circle Fact 13
If two chords intersect in a circle, the product of their segments is equal (product of parts) ab = cd
44
Circle Fact 14
If two secants are drawn from the same external point, outside x whole = outside x whole (product of outside and whole)
45
Circle Fact 15
If a secant and tangent are drawn from the same external point, tangent squared = outside x whole a2 = bc