Vocabulary For Chapter 10 Geometry

Front 1

Theorem 10.1

Back 1

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

Front 2

Theorem 10.2

Back 2

Tangent segments from a common external
point are congruent

Front 3

Theorem 10.3

Back 3

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

Front 4

Theorem 10.4

Back 4

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

Front 5

Theorem 10.5

Back 5

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

Front 6

Theorem 10.6

Back 6

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

Front 7

Theorem 10.7
Measure of an Inscribed Angle Theorem

Back 7

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

Front 8

Theorem 10.8

Back 8

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

Front 9

Theorem 10.9

Back 9

If a right triangle is inscribed in a circle then the hypotenuse s is a diameter of the circle. Conversely,if one side of an inscribed triangle is a diameter of the circle, then the tirangle is a right triangle and the angle opposite the diameter is the right angle

Front 10

Theorem 10.10

Back 10

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

Front 11

Theorem 10.11

Back 11

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

Front 12

Theorem 10.12

Back 12

If two chords intersect in the interior
of a circle then the measure of
each angle is one half the sum of
the measure of the arcs intercepted
by the angle and its vertical angle

Front 13

Theorem 10.13

Back 13

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 one half the difference
of the measure of the intercepted arcs

Front 14

Theorem 10.14

Back 14

If two chords intersect in the interior
of 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

Front 15

Theorem 10.15

Back 15

If 2 secant segments share the same endpoint outside of a O, then the product of the length of 1 secant segment & the length of its external segment =s the product of the length of the other secant segment and the length of its external segment

Front 16

Theorem 10.16

Back 16

If a secant segment and a tangent segment share and endpoint outside a circle, the the product of the lenth of the secant segment and the length of its external segment equals the square of the length of the tangent segment

Front 17

Circle

Back 17

The set of all points in a plane that are
equidistant from a given point,
called the center

Front 18

Radius

Back 18

The distance from the center to a point
on the circle is the radius of the circle

Front 19

Congruent

Back 19

Two circle are congruent if they have the same radius

Front 20

Diameter

Back 20

The distance across the circle, through its
center of the circle and a point on the circle

Front 21

Chord

Back 21

A chord is a segment whose endpoints are
points on the circle

Front 22

Diameter

Back 22

A diameter is a chord that passes through
the center of the circle

Front 23

Secant

Back 23

A secant is a like that intersects a circle in two points

Front 24

Tangent

Back 24

A tangent is a line in the plane of a circle
that intersects the cicle in exactly one point

Front 25

Tangent circle

Back 25

Coplanar circles that intersect in one point

Front 26

Concentric

Back 26

Coplanar circles that have a common center

Front 27

Common tangent

Back 27

A line or segment that is tangent to two coplaner circles

Front 28

Interior of a circle

Back 28

Consists of the points that are inside
of the circle

Front 29

Exterior of a circle

Back 29

Consists of the points that are outside the circle

Front 30

Point of tangency

Back 30

The point at which a tangent line
intersects the circle to which it is tangent

Front 31

Central angle

Back 31

An angle whose vertex is the center
of a circle

Front 32

Minor arc

Back 32

The arc that is made when a circle that
is divided by an angle is less than 180 degrees

Front 33

Major arc

Back 33

The larger arc that is made when a
circle is divded by an angle

Front 34

Semicircle

Back 34

When the endpoints of an arc are the
endpoints of a diameter

Front 35

Measure of a minor arc

Back 35

The measure of central angle when
a circle is cut by an angle

Front 36

Measure of a major arc

Back 36

The difference between 360 degrees
and the measure of its associated minor arc

Front 37

Postulate 26
Arc Addition Postulate

Back 37

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

Front 38

Congruent arcs

Back 38

Two arcs of the same circle of of
congruent circle that have the same measure

Front 39

Inscribed angle

Back 39

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

Front 40

Intercepted arc

Back 40

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

Front 41

Inscribed Circle

Back 41

The largest possible circle that can
be drawn interior to a plane figure

Front 42

Circumscribed Circle

Back 42

Circle which passes through all the
vertices of a polygon

Front 43

Tangent segment

Back 43

A segment of a tangent that is before
hitting the point of tangency

Front 44

Secant segment

Back 44

A segment of a secant

Front 45

External secant segment

Back 45

The outside section of a secant that has
yet to intersect with the circle

Front 46

Standard equation of a circle

Back 46

Using the distance formula to find
the radius of a circle on a coordinate
plan using the center of the circle and
an outside point

Front 47

Locus

Back 47

The set of all points in a plane that
satisfy a five condition or a set
of given conditions