Chapter 10 Test

Question 1

Area formula

Answer 1

A=pi*r^2

Question 2

Cirumference

Answer 2

C=2pir=pi*diameter

Question 3

Arc

Answer 3

A piece of the circle; it is made up of two points on a circle and all the points of the circle needed to connect those two points by a single path

Question 4

Arc measure

Answer 4

The number of degrees it occupies in the circle. Since circles are 360, an arc is at most 360

Question 5

Central Angle

Answer 5

An angle formed by two radii. It is equal to the measure of the arc it creates

Question 6

Arc length

Answer 6

The fraction of the circle’s circumference occupied by the arc; expressed in linear units such as feet, centimeters, or inches

Question 7

Circle

Answer 7

The set of all points equidistant from one central point, called the center

Question 8

Sector

Answer 8

The region of the circle created by a central angle.

Question 9

Combined ratio of the sector and central angle

Answer 9

area of sector measure of central angle
_____________ = ________________________
area of circle 360*

Question 10

Arc length formula

Answer 10

Arc length= measure of the central angle
__________________________ C
360*

Question 11

Sector area formula

Answer 11

Area of sector= measure of central angle
______________________ (Area of circle)
360*
OR

Area of sector= arc length
______________ (Area of circle)
Circumference

Question 12

Congruent circles

Answer 12

If two circles are congruent, then they have the same radii

Question 13

Concentric circles

Answer 13

two or more coplanar circles with the same center

Question 14

Exterior vs. interior points

Answer 14

• If the distance to a point is less than the radius, then the point is on the interior of the circle
• If the distance to a point is greater than the radius, then the point is on the exterior of the circle
• If the distance to a point is equal to the radius, then the point is on the circle

Question 15

Distance from a chord to the center

Answer 15

The distance from the center of the chord is the measure of the perpendicular segment from the center to the chord.

Question 16

Theorem #1

Answer 16

If a radius is perpendicular to a chord, then it bisects the chord

Question 17

Theorem #2

Answer 17

If a radius bisects a chord that is not a diameter, then it is perpendicular to that chord
(converse of theorem #1)

Question 18

Theorem #3

Answer 18

The perpendicular bisector of a chord passes through the center of a circle

Question 19

Equidistance theorem #1

Answer 19

Points on the perpendicular bisector of a segment are equidistant from the endpoints of that segment.

Question 20

Equidistance theorem #2

Answer 20

If two points are equidistant from the endpoints of a segment, then they are on the perpendicular bisector of that segment.

Question 21

Theorem #4

Answer 21

If two chords of a circle are equidistant from the center, then they are congruent

Question 22

Theorem #5

Answer 22

If two chords of a circle are congruent, then they are equidistant from the center of the circle

Question 23

Minor Arcs

Answer 23

Less than 180*, named with two letters

Question 24

Major arcs

Answer 24

Greater than 180*, named with 3 letters

Question 25

Semicircles

Answer 25

Equal to 180*, named with 3 letters

Question 26

Congruent arcs

Answer 26

Arcs that have the same measure AND are parts of the same circle or congruent circles

Question 27

Super theorem

Answer 27

In the same or congruent circles…

congruent chordscongruent arc lengthscongruent central angles

Question 28

Tangent

Answer 28

A tangent line (or segment) intersects a circle at exactly one point. This point is called the point of tangency.

Question 29

Secant

Answer 29

A secant line (or segment) intersects a circle at exactly two points. The interior part of a secant is a chord.

Question 30

Postulates

Answer 30

A tangent line is perpendicular to the radius drawn to the point of tangency.

If a line it perpendicular to a radius at its point of contact with the circle, then it is tangent to the circle.

Question 31

Two-tangent theorem

Answer 31

If two tangent segments are drawn to a circle from an external point, then those segments are congruent

Question 32

Tangent circles

Answer 32

Circles that intersect each other at exactly one point. There’s external and internal (one inside of the other).

Question 33

Common tangent

Answer 33

A line that intersects two circles at exactly one point each

Question 34

Steps for external tangent problems

Answer 34

Step 1: Connect the centers
Step 2: Draw the radii to the points of tangency
Step 3: From the center of the smaller circle, draw a line parallel to the common tangent. This creates a rectangle.
Step 4: Use P.T. and properties of rectangles

Question 35

Distance between two circles

Answer 35

The distance between two circles lies along the line connecting their centers

Question 36

Steps for internally tangent problems

Answer 36

Draw them

Question 37

The vertex of an angle can be in one of FOUR places:

Answer 37

• The center of the circle
  • On the circle
  • Inside the circle but not at the center
• Outside the circle

Question 38

Inscribed angles

Answer 38

Equal to half the measure of its intercepted arc

Question 39

Tangent-chord angles

Answer 39

Formed by a tangent and a chord, also equal to the measure of half the intercepted arc

Question 40

Chord-chord angle

Answer 40

Formed by two chords that intersect inside (but not at the center of) a circle; equal to half the sum of the arcs intercepted by the chord­-chord angle and its vertical angle
1/2mA+1/2mB=beta

Question 41

secant-secant, tangent-tangent, and secant-tangent angles

Answer 41

VERTICES OUTSIDE THE CIRCLE

Equal to half the difference of the intercepted arcs: θ = (1/2)(b - a) BASICALLY θ = (1/2)(bigger arc - smaller arc)

Question 42

Theorem 1

Answer 42

If two inscribed or tangent­chord angles intercept the same or congruent arc(s), then they are congruent

Question 43

Theorem 2

Answer 43

An angle inscribed in a semicircle is right

Question 44

Theorem 3

Answer 44

The sum of the measures of a tangent-tangent angle and it’s minor arc is 180*

Question 45

Inscribed Polygon

Answer 45

A polygon is inscribed in a circle if all of it’s vertices lie on the circle

Question 46

Circumcenter

Answer 46

The center of a circle circumscribed about a polygon

Question 47

Circumscribed Polygon

Answer 47

A polygon is circumscribed about a circle if each of its sides is tangent to the circle

Question 48

Incenter

Answer 48

The center of a circle inscribed in a polygon

Question 49

Apothem

Answer 49

The segment which joins the center of a regular polygon to the midpoint of one of the sides. If the polygon circumscribes the circle, the apothem is a radius of the circle

Question 50

Theorem 3

Answer 50

If a quadrilateral is inscribed in a circle, its opposite angles are supplementary

Question 51

Theorem 4

Answer 51

If a parallelogram is inscribed in a circle, it must be a rectangle

Question 52

Chord-chord power theorem

Answer 52

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

Question 53

Tangent-secant theorem

Answer 53

If a tangent segment and a secant segment are drawn from an external point to a circle, then the square of the measure of the tangent segment is equal to the product of the measures of the entire secant segment and its external part
t^2=sxe

Question 54

Secant-secant power theorem

Answer 54

If two secant segments are drawn from an external point to a circle, then the product of the measures of one secant segment and its external point is equal to the product of the other secant segment and its external part