Chapter 12: Circles

Question 1

Definition 60: A circle is

Answer 1

the set of all points in a plane that are at a given distance from a given point, called the center, in the plane.

Question 2

Definition 61: A radius is

Answer 2

a line segment that joins the center of the circle to a point of the circle.

Question 3

Postulate 17: All radii of the same circle are

Answer 3

congruent

Question 4

Definition 62: A chord of circle is

Answer 4

a line segment that joins two points of the circle.

Question 5

Definition 63: Diameter of a circle is

Answer 5

a chord that contains the center

Question 6

Definition 64: A tangent line is

Answer 6

a line which interests a circle at exactly one point; the point of contact of called the point of tangency.

Question 7

Definition 65: A secant line is

Answer 7

a line which interests a circle at two different points

Question 8

Theorem 61: If a line through the center of a circle is perpendicular to a chord, it

Answer 8

also bisects the cord.

Question 9

Theorem 62: In the same circle, congruent chords are equidistant (the same distance) from

Answer 9

the center of the circle.

Question 10

Theorem 63: In the same circle, chords equidistant form the center of the circle are

Answer 10

congruent.

Question 11

Theorem 64: If a radius is drawn to the point of tangency of a tangent line, then

Answer 11

the radius is perpendicular to the tangent line.

Question 12

Theorem 65: If a radius is perpendicular to a line at the point where the line intersects a circle, then

Answer 12

the line is a tangent line.

Question 13

Definition 66: A tangent segment is

Answer 13

a line segment that has a point on the tangent line and the point of tangency as an end point.

Question 14

Theorem 66: If two tangent segments are drawn to a circle from the same exterior point, then

Answer 14

they are congruent.

Question 15

Definition 67: An arc is

Answer 15

a portion of a circle consisting of two end points and the set of points on the circle that lie between those points.

Question 16

Definition 68: A central angle is

Answer 16

an angle whose vertex is at the center of the circle.

Question 17

Definition 69: The degree measure of a minor arc is the

Answer 17

measure of its central angle.

Question 18

Definition 70: The circumference of a circle is the

Answer 18

distance around the circle, expressed in linear units of measurement (inches, centimeters, etc.).

Question 19

Theorem 67: Arc Length-Degree Measure Proportion:

Answer 19

Arc Length/Circumference = Degree Measure/360

Question 20

Postulate 18: Arc Addition Postulate: If P is on AB, then

Answer 20

mAP + mPB = mAB.

Question 21

Definition 71: Congruent arcs are

Answer 21

arcs in the same or congruent circle which have the same degree measure.

Question 22

Definition 72: The midpoint of an arc is the

Answer 22

point on the arc which divides the arc into two congruent arcs.

Question 23

Theorem 68: If two chords of the same or congruent circles are congruent, then

Answer 23

their minor arcs are congruent.

Question 24

Theorem 69: If two minor arcs of the same or congruent circles are congruent, then

Answer 24

their intersecting chords are congruent.

Question 25

Theorem 70: In a circle, a diameter drawn perpendicular to a chord bisects the minor arc that

Answer 25

the chord intercepts.

Question 26

Definition 73: An inscribed angle is

Answer 26

an angle whose vertex is on a circle and whose sides are chords (or secants) of the circle.

Question 27

Theorem 71: An inscribed angle is

Answer 27

equal in measure to one-half the measure of its intercepted arc.

Question 28

Corollary 71.1: Inscribed angles that intercept the same or congruent arcs are

Answer 28

congruent.

Question 29

Corollary 71.2: An inscribed angle that intercepts a semicircle is a

Answer 29

right angle.

Question 30

Theorem 72: The measure of an angle formed by a tangent and a chord drawn to the point of tangency is

Answer 30

equal to one-half the measure of the intercepted arc.

Question 31

Theorem 73: The measure of an angle formed by two chords (or secants) intersecting in the interior of a circle is

Answer 31

equal to one-half the sum of the measures of the two intercepted arcs.

Question 32

Theorem 74: The measure of an angle formed by two secants (or tangents) intersecting in the exterior of a circle is

Answer 32

equal to one-half the difference of the measures of the two intercepted arcs.

Question 33

Theorem 75: If two chords intersect in the interior of a circle, the product of the lengths of the segments of one chord is

Answer 33

equal to the product of the lengths of the segments of the other.

Question 34

Theorem 76: If two secant segments are drawn to a circle from the same exterior point, then the product of the lengths of one secant segment and its external segment is

Answer 34

equal to the product of the lengths of the other secant segment and its external segment.

Question 35

Theorem 77: If a tangent segment and a secant segment are drawn to a circle from the same exterior point, then the square of the length of the tangent segment is

Answer 35

equal to the product of the lengths of the secant segment and its external segment.