geometry: chapter 9

Question 1

circle

Answer 1

a set of points in a plane equidistant from a given point in the plane

Question 2

center

Answer 2

the given point

Question 3

radius

Answer 3

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

Question 4

chord

Answer 4

segment whose endpoints lie in the circle

Question 5

secant

Answer 5

a line that contains a chord

Question 6

diameter

Answer 6

chord that contains the center of the circle

Question 7

tangent

Answer 7

line in the plane of a circle that intersects the circle at exactly 1 point

Question 8

point of tangency

Answer 8

point that the tangent intersects the circle

Question 9

sphere

Answer 9

set of all points in space at a given distance from a given point

Question 10

congruent circles

Answer 10

have congruent radii

Question 11

concentric circles

Answer 11

circles that line in same plane and have the same center

Question 12

concentric spheres

Answer 12

spheres that have same center

Question 13

inscribed/ circumscribed polygon

Answer 13

vertices of the polygon lie on the circle

Question 14

Theorem 9-1

Answer 14

If a line is tangent to a circle then the line is perpendicular to the radius drawn to the point of tangency.

Question 15

Corollary to Theorem 9-1

Answer 15

Tangents to a circle from a point are congruent

Question 16

Theorem 9-2

Answer 16

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 17

common tangent

Answer 17

a line that is tangent to each of two coplanar circles

Question 18

common internal tangent

Answer 18

intersects the segment joining the centers of the circles

Question 19

common external tangent

Answer 19

does not intersect the segment joining the centers

Question 20

tangent circles

Answer 20

coplanar circles that are tangent to the same line at the same point

Question 21

central angle

Answer 21

angle with its vertex at the center of the circle

Question 22

minor arc

Answer 22

part of circle that is smaller than half

Question 23

major arc

Answer 23

part of circle that is greater than half

Question 24

semicircle

Answer 24

arc with the endpoints at the diameter

Question 25

postulate 16: Arc Addiction Postulate

Answer 25

the measure of the arc formed by two adjacent arcs is the sum of the measures of these two arcs

Question 26

adjacent arcs

Answer 26

arcs that have exactly one common endpoint

Question 27

congruent arcs

Answer 27

arcs in the same circle, or congruent circles that have equal measure

Question 28

theorem 9-3

Answer 28

in the same circle or in congruent circles, two minor arcs are congruent if and only if their central angles are congruent.

Question 29

Theorem 9-4

Answer 29

In the same circle or in congruent circles:

1) congruent arcs have congruent chords
2) congruent chords have congruent arcs

Question 30

Theorem 9-5

Answer 30

A diameter that is perpendicular to a chord bisects the chord and its arc

Question 31

Theorem 9-6

Answer 31

In the same circle or in congruent circles

1) chords equally distant from the center are congruent
2) congruent chords are equally distant from the center

Question 32

inscribed angles

Answer 32

an angle whose vertex is on a circle and whose sides contain chords of the circle

Question 33

Theorem 9-7

Answer 33

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

Question 34

Corollary 1 of theorem 9-7

Answer 34

if two inscribed angles intercept the same arc, then the angles are congruent

Question 35

corollary 2 of theorem 9-7

Answer 35

an angle inscribed in a semicircle is a right angle

Question 36

corollary 3 of theorem 9-7

Answer 36

if a quadrilateral is inscribed in a circle, then its opposite angles are supplementary

Question 37

Theorem 9-8

Answer 37

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

Question 38

Theorem 9-9

Answer 38

The measure of an angle formed by two chords that intersect inside a circle is equal to half the sum of the measures of the intercepted arcs

Question 39

theorem 9-10

Answer 39

The measure of an angle formed by two secants, two tangents, or a secant and a tangent drawn from a point outside a circle is equal to half the difference of the measures of the intercepted arcs.

Question 40

theorem 9-11

Answer 40

when two chords intersect inside a circle, the product of the segments of one chord equals the product of the segments of the other chord

Question 41

Theorem 9-12

Answer 41

When two secant segments are drawn to a circle from an external point, the product of one secant segment and its external segment equals the product of the other secant segments and its external segment.

Question 42

Theorem 9-13

Answer 42

when a secant segment and a tangent are drawn to a circle from an external point, the product of the secant segment and its external segment is equal to the square of the tangent segment