Chapter 10

Question 0

Chord

Answer 0

A segment whose endpoints are on a circle

Question 1

Cirle

Answer 1

Set of. All points in a plane that are equidistant from a certain point called the center. The points inside the circle form it’s interior. The points outside the circle form it’s exterior.

Question 2

Diameter

Answer 2

A chord that passes through the center

Question 3

Radious

Answer 3

A segment that has a center as one endpoint and a point on the circle as another

Question 4

Tangent

Answer 4

A line that intersects a circle at exactly one point

Question 5

Point of tangency

Answer 5

The point at which the tangent intersects

Question 6

Secant

Answer 6

A line that intersects a circle at two points

Question 7

Common tangent

Answer 7

A line that is tangent to two circles

Question 8

Common external tangent

Answer 8

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

Question 9

Common internal tangent

Answer 9

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

Question 10

Concentric circles

Answer 10

Circles that have the same center

Question 11

Congruent circles

Answer 11

Circles with congruent radii or diameters

Question 12

Thm 10.1

Answer 12

If a line is tangent to a circle then it is perpendicular to the radio us drawn to the point of tangency

Question 13

Thm 10.2

Answer 13

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

Question 14

Thm 10.3

Answer 14

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

Question 15

Inscribed circle

Answer 15

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

Question 16

Circumscribed circle

Answer 16

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

Question 17

Central angle

Answer 17

An angle whose vertex is the center of a circle and whose sides pass through a pair of points on the circle

Question 18

Minor arcs

Answer 18

A shorter ace joining two points together on a circumference

Question 19

Measure of a minor arc

Answer 19

The smaller arc when a circle is divided unequally

Question 20

Semi circle

Answer 20

A circle cut on the diameter

Question 21

Major arc

Answer 21

A longer arc joining two points together on a circumference

Question 22

Measure of a major arc

Answer 22

The bigger arc when a circle is divided unequally

Question 23

Adjacent arc

Answer 23

Two arcs on a circle that share exactly one endpoint

Question 24

Arc addition postulate

Answer 24

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

Question 25

Congruent arcs

Answer 25

Arcs with the same measure on the same congruent circles

Question 26

Thm 10.4

Answer 26

In the same circles, or in congruent circles, two arcs are congruent iff their central angles are congruent

Question 27

Thm 10.13

Answer 27

If a tangent and a chord intersect at a point on a circle then the measure of each angle formed is half the measure of the intercepted arc

Question 28

Thm 10.14

Answer 28

If two chords intersect in the interior of a circle, then the measure of each angle is half the sum of the measures of the arcs intercepted by the angle, and it's verticals angle

Question 29

Thm 10.15

Answer 29

If a tangent and a secant, two tangents, or two secants, intersect in the exterior of a circle then the measure of the angle formed is half the difference of the measures of the intercepted arcs

Question 30

Thm 10.5

Answer 30

In the same circle or in congruent circles, two minor arcs are congruent iff their corresponding chords are congruent

Question 31

Thm 10.6

Answer 31

If a diameter of a circle is perpendicular to a chord, then the diameter bisects it's chord at the arc

Question 32

Thm 10.7

Answer 32

If a chord is perp to a bisector of another chord, then it is the diameter

Question 33

Thm 10.8

Answer 33

In the same circle, or in congruent circles, two chords are congruent iff they are equidistant from the center

Question 34

Inscribed angle of a circle

Answer 34

An angle who's vertex is on the circle and sides are part of the circle

Question 35

Intercepted arc

Answer 35

Te arc that lies in the interior of an inscribed angle

Question 36

Thm 10.9

Answer 36

If an angle is inscribed in a circle then it's measure is half the measure of it's intercepted arc

Question 37

Thm 10.10

Answer 37

If two inscribed angles of a circle intercept the same arc, then the angles are congruent

Question 38

Thm 10.11

Answer 38

An angle that is inscribed in a circle is a right angle iff it's corresponding arc is a semicircle

Question 39

Thm 10.12

Answer 39

A quadrilateral can be inscribed in a circle iff it's opposite angles are supplementary