Chapter 10

Question 1

What is a tangent?

Answer 1

a line that intersects a circle at exactly one point

Question 2

Theorem 12-1:

if a line is tangent to a circle then the line is…

Answer 2

perpendicular to the radius drawn to the point of tangency

Question 3

Theorem 12-2:

if a line in the plane of a circle is perpendicular to a radius at its endpoint on the circle…

Answer 3

then the line is tangent to the circle

Question 4

Theorem 12-3:

The two segments tangent to the outside of a circle are…

Answer 4

congruent

Question 5

What is a chord?

Answer 5

A segment whose endpoints are on a circle

Question 6

What is a diameter?

Answer 6

A chord that goes through the center of a circle

Question 7

What is an arc?

Answer 7

pieces of a circle

Question 8

what is a minor arc?

Answer 8

an arc that is less than 180 degrees

Question 9

what is a major arc?

Answer 9

an arc that is more than 180 degrees

Question 10

what is a semicircle?

Answer 10

an arc that is exactly 180 degrees

Question 11

what is a central angle?

Answer 11

an angle made up of two segments whose vertex is the center of the circle

Question 12

Theorem 12-4:

within a circle or in congruent circles… (three things)

Answer 12

1. Congruent central angles have congruent chords
2. Congruent chords have congruent arcs
3. Congruent arcs have congruent central angles

Question 13

Theorem 12-5:

within a circle or congruent circles… (two things)

Answer 13

1. Chords equidistant from the center are congruent

2. Congruent chords are equidistant from the center

Question 14

Theorem 12-6:

In a circle, a diameter that is perpendicular to a chord…

Answer 14

bisects the chord and its arcs

Question 15

Theorem 12-7:

In a circle, a diameter that bisects a chord (that is not a diameter)…

Answer 15

is perpendicular to the chord

Question 16

Theorem 12-8:

In a circle, the perpendicular bisector of a chord contains…

Answer 16

the center of the circle

Question 17

What is an inscribed angle?

Answer 17

an angle whose sides are chords and whose vertex is ON the circle

Question 18

Theorem 12-9:

the measure of an inscribed angle is…

Answer 18

half the measure of its intercepted arc

Question 19

Two inscribed angles that intercept the same arc are…

Answer 19

congruent

Question 20

An angle inscribed in a semicircle is always…

Answer 20

a right angle

Question 21

The opposite angles of a quadrilateral inscribed in a circle are…

Answer 21

supplementary

Question 22

Theorem 12-10:

The measure of an angle formed by a tangent and a chord is…

Answer 22

half the measure of an intercepted arc

Question 23

What is a secant?

Answer 23

a chord that extends outside the circle, and has two endpoints lying on the circle

Question 24

Theorem 12-11:

the measure of an angle formed by two lines that… (two things, one is inside, other is outside)

Answer 24

1. intersect INSIDE a circle is half the SUM of the measures of the intercepted arcs (but not the center)
2. intersect OUTSIDE the circle is half the DIFFERENCE of the measures of the intercepted arcs

Question 25

Trick for 2 tangent circles

Answer 25

angle + arc = 180

Question 26

Theroem 12-12 (Part 1): how do you find part of the length of two chords intersecting inside a circle?

Answer 26

the product of the pieces of one chord is equal to the product of the pieces of the other chord

Question 27

Theorem 12-12 (Part 2): two secants intersect outside a circle

Answer 27

(whole secant) (outside piece) = (whole secant) (outside piece)

Question 28

Theorem 12-12 (Part 3): a tangent and a secant intersect outside a circle

Answer 28

(whole secant) (outside piece) = (tangent)^2

Question 29

Theorem 12-13: what is the equation of a circle?

Answer 29

(x-h)^2 + (y-k)^2 = r^2 where r is the radius and (h,k) is the center this is known as standard form

Question 30

How do you complete the square and get a circle in Standard Form?

Answer 30

1. Gather the x terms and y terms so they are next to each other in the equation. Get the constant on the other side. 2. Look at the coefficients of the x term and the y term. Divide the coefficients by 2 and square them. Add those numbers to BOTH sides 3. Factor the x-trinomial and the y-trinomial. Both must factor into the same parenthesis twice. ex: (x-4)^2 The circle is not un the correct form.

Question 31

If there is a plus (+) in the equation it is a...

Answer 31

circle!

Question 32

if there is a minus (-) the the equation it is a...

Answer 32

ellipse or hyperbola! don't fall for those!

Question 33

Theorem 10-9: Circumference of a Circle

Answer 33

the circumference of a circle is π times the diameter C= πd *OR* 2πr

Question 34

What is an Arc Length?

Answer 34

a fraction of the circle's circumference

Question 35

Theorem 10-10: Arc Length

Answer 35

the length of an arc of a circle is the product of the ratio of the measure of the arc and the circumference of the circle length = n ------ x 2πr 360

Question 36

what is "Exact Area"

Answer 36

the answer in terms of pi (π)

Question 37

Theorem 10-11: Area of a Circle

Answer 37

A = πr^2

Question 38

Theorem 10-12: Area of a Sector of a Circle

Answer 38

Sector Area = n ------ x πr^2 360