Chapter 11

Question 1

chord

Answer 1

a segment whose endpoints are points on a circle

Question 2

secant

Answer 2

a line in the plane of a circle that intersects the circle

Question 3

point of tangency

Answer 3

a point on the line that intersects the circle in exactly one point

Question 4

Theorems 11.1 and 11.2

“properties of tangents”

Answer 4

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

In a plane, if a line is perpendicular to a radius of a circle at its endpoint on the circle, then the line is tangent to the circle.

Question 5

tangent segment

Answer 5

touches a circle at one of the segment’s endpoints and lies in the line that is tangent to the circle at that point

Question 6

Theorem 11.3

Answer 6

If two segments from the same point outside a circle are tangent to the circle, then they are congruent.

Question 7

minor arc

Answer 7

if a measure of an angle is less than 180, then all the points on that angle form a minor arc
arcs are denoted by A⌒B
(an angle that has a vertex at the very center of the circle)

Question 8

major point

Answer 8

all the other points that do not lie on A⌒B, form a major arc (these require 3 points to denote)

Question 9

measure of a major arc

Answer 9

the difference of 360` and the measurement of the related minor arc

Question 10

semicircle

Answer 10

an arc whose central angle measures 180`, named by three points

Question 11

Postulate 16 “Arc Addition Postulate”

Answer 11

The measure of an arc formed by two adjacent arcs is the sum of the measured of the two arcs.

Question 12

congruent circles

Answer 12

two circles that have the same radius

Question 13

congruent arcs

Answer 13

two arcs of the same circle or of congruent circles if they have the same measure.

Question 14

arc length

Answer 14

a portion of the circumference of a circle.
You can write a proportion to find arc length:
arc length of A⌒B = mA⌒B
———– of 2(3.14)(radius)
360`

Question 15

Arc length

Answer 15

In a circle, the ratio of the length of a given arc to the circumference is equal to the ratio of the measure of the arc to 360`

Question 16

Theorem 11.4 “diameter perpendicular to a chord”

Answer 16

If a diameter of a circle is perpendicular to a chord, then the diameter bisects the chord and its arc

Question 17

Theorem 11.5 “chord perpendicular to another chord”

Answer 17

If one chord is perpendicular bisector of another chord, then the first chord is a diameter.

Question 18

Theorem 11.6 “in the same circle or in congruent ones”

Answer 18

In the same circle, or in congruent circles:

If two chords are congruent, then their corresponding minor arcs are congruent.

If two minor arcs are congruent, then their corresponding chords are congruent.

Question 19

inscribed angle

Answer 19

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

Question 20

intercepted arc

Answer 20

the arc that lies in the interior of an inscribed angle and has endpoints of the angle

Question 21

Theorem 11.7 “measure of an inscribed angle”

Answer 21

If an angle is inscribed in a circle, then its measure is half the measure of its intercepted arc.

Question 22

inscribed

Answer 22

if all the vertices of a polygon lie on a circle

Question 23

circumscried

Answer 23

if all the vertices of a polygon lie on a circle and the circle is circumscribed about the polygon

Question 24

Theorem 11.8 “inscribed and circumscribed”

Answer 24

If a triangle inscribed in a circle is a right triangle, then the hypotenuse is a diameter of the circle.
If a side of a triangle inscribed in a circle is a diameter of the circle, then the triangle is a right triangle.

Question 25

Theorem 11.9 “quadrilateral inscribed”

Answer 25

If a quadrilateral can be inscribed in a circle, then its opposite angles of a quadrilateral are supplementary.

If the opposite angles of a quadrilateral are supplementary, then the quadrilateral can be inscribed in a circle

Question 26

Theorem 11.10 “properties of chords”

Answer 26

If two chords intersect inside a circle, then the measure of each angel formed is one half the sum of the measures of the arcs intercepted by the angle and its vertical angle.

Question 27

Theorem 11.11 “intersecting chords”

Answer 27

If two chords intersect inside a circle, then the product of the lengths of the segments of one chord is equal to the product of the lengths of the segments of the other chord

Question 28

standard equation of a circle

Answer 28

In the coordinate plane, the standard equation of a circle with center a (h,k) and radius r is:
(x - h)^2 + (y - k)^2 = r^2

Question 29

rotation

Answer 29

a transformation in which a figure is turned about a fixed point. the fixed point is the center of rotation

Question 30

angle of rotation

Answer 30

Rays drawn from the center of rotation to a point and its image form an angle

Question 31

Rotational symmetry

Answer 31

if a figure in a plane can be mapped onto itself by a rotation of 180` or less