Chapter 10

Question 1

Circle

Answer 1

Set of all points in a plane that are equidistant from a given point called the center.

Question 2

Interior of a circle

Answer 2

Points inside the circle.

Question 3

Exterior of a circle

Answer 3

Points outside a circle.

Question 4

Chord

Answer 4

A segment whose endpoints are on the circle.

Question 5

Diameter

Answer 5

A chord that passes through the center of a circle.

Question 6

Radius

Answer 6

Segment whose endpoints consist of the center of the circle and a point on the radius (Measure of the distance)

Question 7

Tangent

Answer 7

If a line intersects a circle at exactly one point, the line is a tangent of a circle. This point of intersection is called the point of tangency.

Question 8

Secant

Answer 8

If a line intersects a circle at two points, then the line is a secant. (Secants are ALWAYS lines, whereas tangent lines can be segments, lines, etc.)

Question 9

Common Tangent

Answer 9

Tangent line that is tangent to two circles.

Question 10

Common External Tangent

Answer 10

A common tangent that does not intersect the segment that join the centers of the circles.

Question 11

Common Internal Tangent

Answer 11

A common tangent that intersects the segment that joins the centers of the circles.

Question 12

Concentric Circles

Answer 12

Circles that have the same center. (Good for counterexamples)

Question 13

Congruent Circles

Answer 13

Circles with congruent radii or diameters.

Question 14

Theorem 10.1

Answer 14

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

Question 15

Thoerem 10.2

Answer 15

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

Question 16

Theorem 10.3

Answer 16

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

Question 17

Inscribed

Answer 17

A circle is inscribed in a polygon if each side of the polygon is tangent to the circle.

Question 18

Circumscribed

Answer 18

A circle is circumscribed about a polygon if each vertex of the polygon lies on the circle.

Question 19

Central Angle

Answer 19

An angle who’s vertex is the center of the circle.

Question 20

Minor Arc

Answer 20

Consists of the endpoints of the central angle and all points on the circle that are in the interior of the central angle.

Question 21

Measure of a Minor Arc

Answer 21

The measure of the central angle measures less than 180.

Question 22

Semicircle

Answer 22

An arc whose endpoints are t endpoints of the diameter.

Question 23

Major Arc

Answer 23

Consists of the endpoints of the central angle and all points on the circle that lie in the exterior of the central angle.

Question 24

Measure of a Major Arc

Answer 24

Always equal to 360- the measure of the associated minor arc.

Question 25

Adjacent Arcs

Answer 25

Two arcs of the same circle are adjacent if they intersect at exactly one point.

Question 26

Arc Addition Postulate

Answer 26

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

Question 27

Congruent Arcs

Answer 27

In the same circle or in congruent circles, two arcs are congruent if they have the same measure.

Question 28

Theorem 10.4

Answer 28

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

Question 29

Theorem 10.5

Answer 29

In the same circle or congruent circles, two minor arcs are congruent if and only if their corresponding chords are congruent.

Question 30

Theorem 10.6

Answer 30

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

Question 31

Theorem 10.7

Answer 31

If chord AB is a perpendicular bisector of another chord, then AB is a diameter.

Question 32

Theorem 10.8

Answer 32

In the same circle or in congruent circles, two chords are congruent if and only if they are equidistant from the center.

Question 33

Inscribed Angle

Answer 33

An angle whose sides are chords of a circle.

Question 34

Intercepted Arc

Answer 34

The arc that lies in the interior of an inscribed angle.

Question 35

Theorem 10.9

Answer 35

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

Question 36

Theorem 10.10

Answer 36

If two inscribed angles of a circle intercept the same arc, then those angles are congruent. (THESE TRIANGLES ARE ALWAYS SIMILAR, SOMETIMES CONGRUENT.)

Question 37

Theorem 10.11

Answer 37

An angle that is inscribed in a circle is a right angle if and only if its corresponding arc is a semicircle.

Question 38

Theorem 10.12

Answer 38

A quadrilateral can be inscribed in a circle if and only if its opposite angles are supplementary.