unit 9: circles Flashcards

1
Q

circle

A

the set of points in a plane at a given distance from a given point in that plane

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2
Q

center

A

the given point of a circle

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3
Q

the radius

A

the given distance of a circle

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4
Q

a radius

A

any segment that joins the center to a point of the circle

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5
Q

chord

A

a segment whose endpoints lie on a circle

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6
Q

secant

A

a line that contains a chord

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7
Q

diameter

A

a chord containing the circle’s center

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8
Q

tangent

A

a line in the plane of a circle that intersects the circle at only the point of tangency

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9
Q

the point of tangency

A

the point where the tangent intersects with the circle

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10
Q

sphere

A

the set of points in space at a given distance from the circle at the set of the set radius from the circle

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11
Q

congruent circles & spheres

A

circles or spheres that have congruent radii

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12
Q

concentric circles

A

circles in the same plane with the same center

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12
Q

concentric spheres

A

spheres with the same center

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12
Q

a polygon is inscribed in a circle, and…

A

the circle is circumscribed about the polygon

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13
Q

central angle

A

(of a circle): an angle with a vertex at the center

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14
Q

arc

A

an unbroken part of a circle

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15
Q

minor arc

A

the interior of the central angle; the degree of the central angle

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16
Q

major arc

A

the exterior of the central angle; 360-the degree of the minor arc

17
Q

semicircles

A

2 arcs created by the diameter

18
Q

adjacent arcs

A

arcs with one common point

19
Q

inscribed angle

A

an angle with its vertex on a circle and two chords as sides

20
Q

congruent arcs

A

arcs in the same or congruent circles with equal measures

21
Q

arc addition postulate

A

the measure of an arc formed by 2 adjacent arcs is the sum of the measures of both arcs

22
Q

congruent central angles theorem

A

in the same/congruent circle(s), 2 minor arcs are congruent if and only if their central angles are congruent

23
Q

basic equations of circles (3)

A
  1. A= π r^2
  2. c = π d
  3. arc length= (degree of arc x c) / 360
24
Q

perpendicular tangent theorem

A

if a line is tangent to a circle, then it is perpendicular to the radius at the point of tangency

25
Q

perpendicular tangent theorem converse

A

if a line in the plane of a circle is perpendicular to a radius at its outer endpoint, then the line is tangent to the circle

26
Q

external tangents congruence theorem

A

if 2 tangents to a circle share a common point outside the circle, the 2 segments are congruent

27
Q

common tangent

A

a line tangent to each of 2 coplanar circles

28
Q

internal tangent

A

a tangent intersecting the segment joining the centers

29
Q

external tangent

A

a tangent that doesn’t intersect the segment joining the centers

30
Q

tangent circles

A

coplanar circles tangent to the same line at the same point (envision internal and external views)

31
Q

central angle theorem

A

in the same/congruent circle(s),
1. congruent arcs have congruent chords
2. congruent chords have congruent arcs

32
Q

perpendicular chord bisector theorem

A

a diameter that is perpendicular to a chord bisects the chord & its arc

33
Q

equidistant chords theorem

A

in the same/congruent circle(s),
1. chords equally distant from the center(s) are congruent
2. congruent chords are equally distant from the center(s)

34
Q

inscribed angle theorem

A

the measure of an inscribed angle is equal to half the measure of its intercepted arc

35
Q

inscribed angle theorem corollaries

A
  1. if 2 inscribed angles intercept the same arc, the angles are congruent
  2. an angle inscribed in a semicircle is a right angle
  3. if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary
36
Q

tangent & intersected chord theorem

A

the measure of an angle formed by a chord and a tangent is half the measure of the intercepted arc

37
Q

angle inside the circle theorem

A

the measure of an angle formed by the intersection of 2 chords in a circle is equal to 1/2 the sum of the intercepted arcs

38
Q

angle outside the circle theorem

A

the measure of an angle formed by 2 secants, 2 tangents, or a secant and a tangent from a point outside the circle is equal to 1/2 the difference of the intercepted arcs

39
Q

segments of chords theorem

A

when 2 chords intersect inside a circle, the products of 1 chord’s segments equal the products of the other chord’s segments

rs=tu, r/t=u/s

40
Q

segments of secants theorem

A

when 2 secants meet at an external point, the product of 1 secant and its external segment equals the product of the other secants and its external segment

rs=tu, r/t=u/s

41
Q

segments of a tangent and a secant theorem

A

when a secant & tangent meet at an external point, the product of the secant segment and its external segment equal the tangent segment squared

rs=t^2, r/t=t/s