7.3 HW Answers

(0,0)

2

( 3,3)

1

(0, 3)

4

(7, 2)

2

(2, 3)

5225 un

10 un

( 5, 1)

4216 un

8 un

(0, 2)

121 un

2 un

22( 4) 1 4x y

22( 4) 3 9x y

22.25 4.5un 236 9 m

2

135

360 16

6

x

x un

36036

10

10 10

18

2

120 30.78 10

2

3078

A

A un

10tan18

30.78x

x

5un 225A un

9

9 281un

8

10

9

9

8

281A un

272un

Scoring Your Homework

• Count how many problems you missed or didn’t do

• 0-2 missed = 10• 3-4 missed = 9• 5-7 missed = 8• 8-11 missed = 7• 12-14 missed = 6

• 15-18 missed = 5• 19-21 missed = 4• 22-25 missed = 3• 26-28 missed = 2• 29-32 missed = 1• 33-35 missed = 0

Daily Check

1. Graph.

(x – 1)2 + (y +3)2 = 9

8in

2. Find the circumference in terms of pi.

45°

3. Find the arc length ofLeave answers in terms of pi.

12m

A

B

ABª .

8in

4. Find the area in terms of pi.

4m

5. Find the area of the shaded sector. Leave answers in terms of pi.

7.4

What’s The Diameter?

Pg. 15

Introduction to Chords

7.4 – What’s The Diameter?Introduction to Chords

So far you learned that the diameter of a circle is the distance across the center of the circle. This length can be easily measured if the entire circle is in front of you and the center is marked, or if you know the radius of the circle. However, what if you only have part of a circle (called an arc)? Today you will consider a situation that demonstrates the need to learn more about the parts of a circle and the relationship between them.

Term Definition Picture

Minor Arc

Arc of a circle that is less than 180°

P

A

C

Two letters:

AC

Term Definition Picture

Major Arc

Arc of a circle that is more than 180°

P

A

C

3 letters:

B

ABC

Term Definition Picture

Semicircle

Arc of a circle that is 180°

P

A

C3 letters:

B

ABC

Term Definition Picture

Chord

A segment with both endpoints on the circle

P

QA

AQ

7.20 – THE WORLD'S WIDEST TREEThe baobab tree (pronounced bay-O-bab) is a species of tree found in Africa and Australia. It is often referred to as the "world's widest tree" because it has been know to be up to 45 feet in diameter!

While digging at an archeological site, Rafi found a fragment of a fossilized baobab tree that appears to be wider than any tree on record! However, since he does not have the remains of the entire tree, he cannot simply measure across the tree to find its diameter. He needs your help to determine the radius of this ancient tree. Assume that the shape of the tree's cross-section is a circle.

The crease is the perpendicular

bisector of AB

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

then

diameter

bisects

and the diameterEG DF

FH HD and FG GD

If one chord is a _________________ _________ of another chord, then the first chord is the _________________.

PT PR

SQ

then

perpendicularbisector

diameter

andTR SQ

is the diameter

In the same circle, or in congruent circles, two ___________ arcs are congruent iff their corresponding __________ are congruent.

A

B C

D

AB CD

then

minor

chords

AB CD

In the same circle, or in congruent circles, two chords are congruent iff they are _________________ from the __________.

then

equidistant center

EF AB

AB CD

and EG CD

EG EFand

7.21 – GIVEN TWO CHORDSWhat if you know the lengths of two chords in a circle? How can you use the chords to find the center of the circle? Examine the chords provided below in the circles. Using only a compass and straightedge, find the center of each circle.

C

C

7.22 – DIAMETERS BISECTING CHORDSFind the given measure of the arc or chord. Explain your reasoning.

5050 100

61

119119

11

22un

EG

12 7 3 16x x 9 7 16x

9 9x 1x

3 1 16

19 19

38un

7.23 – CONGRUENT CHORDSFind the given measure of the arc or chord. Explain your reasoning.

6

6un

105105

90

90

90

90

90

105

105

105

7.24 – EQUIDISTANT FROM THE CENTERFind the value of x.

3 11 9x x 2 11 9x

2 20x 10x

7 8 3x x 4 8 0x

4 8x 2x