unit 9: circles

Question 1

circle

Answer 1

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

Question 2

center

Answer 2

the given point of a circle

Question 3

the radius

Answer 3

the given distance of a circle

Question 4

a radius

Answer 4

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

Question 5

chord

Answer 5

a segment whose endpoints lie on a circle

Question 6

secant

Answer 6

a line that contains a chord

Question 7

diameter

Answer 7

a chord containing the circle’s center

Question 8

tangent

Answer 8

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

Question 9

the point of tangency

Answer 9

the point where the tangent intersects with the circle

Question 10

sphere

Answer 10

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

Question 11

congruent circles & spheres

Answer 11

circles or spheres that have congruent radii

Question 12

concentric circles

Answer 12

circles in the same plane with the same center

Question 12

concentric spheres

Answer 12

spheres with the same center

Question 12

a polygon is inscribed in a circle, and…

Answer 12

the circle is circumscribed about the polygon

Question 13

central angle

Answer 13

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

Question 14

arc

Answer 14

an unbroken part of a circle

Question 15

minor arc

Answer 15

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

Question 16

major arc

Answer 16

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

Question 17

semicircles

Answer 17

2 arcs created by the diameter

Question 18

adjacent arcs

Answer 18

arcs with one common point

Question 19

inscribed angle

Answer 19

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

Question 20

congruent arcs

Answer 20

arcs in the same or congruent circles with equal measures

Question 21

arc addition postulate

Answer 21

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

Question 22

congruent central angles theorem

Answer 22

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

Question 23

basic equations of circles (3)

Answer 23

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

Question 24

perpendicular tangent theorem

Answer 24

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

Question 25

perpendicular tangent theorem converse

Answer 25

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

Question 26

external tangents congruence theorem

Answer 26

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

Question 27

common tangent

Answer 27

a line tangent to each of 2 coplanar circles

Question 28

internal tangent

Answer 28

a tangent intersecting the segment joining the centers

Question 29

external tangent

Answer 29

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

Question 30

tangent circles

Answer 30

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

Question 31

central angle theorem

Answer 31

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

Question 32

perpendicular chord bisector theorem

Answer 32

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

Question 33

equidistant chords theorem

Answer 33

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)

Question 34

inscribed angle theorem

Answer 34

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

Question 35

inscribed angle theorem corollaries

Answer 35

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

Question 36

tangent & intersected chord theorem

Answer 36

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

Question 37

angle inside the circle theorem

Answer 37

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

Question 38

angle outside the circle theorem

Answer 38

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

Question 39

segments of chords theorem

Answer 39

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

Question 40

segments of secants theorem

Answer 40

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

Question 41

segments of a tangent and a secant theorem

Answer 41

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