Aim: What are properties of a Circle? Course: Applied Geo. In the figure above, two parallel lines...

Aim: What are properties of a Circle? Course: Applied Geo.

In the figure above, two parallel lines are cut by a transversal. If the m6 = 2x – 4 and m3x + 44, find m4.

Aim: What are some interesting points about a circle?!

Do Now:1

3 45 6

7 8

2

What’s the relationship between 6 & 1?

2x – 4 + 3x + 44 = 1805x + 40 = 1805x = 140x = 28

1. m4 = m1 - vertical s

Evaluate 3x + 44, if x = 28:

2. m4 & m6 are supplementary - Interior s on same side of transversal

3(28) + 44 = 1280 = m4

supplementary


Aim: What are some interesting points about a circle?!

Do Now:

Why


1st Qtr

2nd Qtr

3rd Qtr

4th Qtr

The Circle


A circle is the set of all points in a plane equidistant from a given point called the

center.

A circle is the set of all points in a plane equidistant from a given point called the

center.

Introducing the Circle


A

Radius - a segment with one endpoint at the center and the other endpoint on the circle. Ex. OA

B

C

Diameter - a segment that contains the center and has both endpoints on the circle. Example BC

O

Anatomy of Circle


O A

B

C

The Radius of a circle is 1/2 the length of the Diameter

The Radius of a circle is 1/2 the length of the Diameter

The Diameter is twice the length of the Radius.

The Diameter is twice the length of the Radius.

The Center is the midpoint of any Diameter.

The Center is the midpoint of any Diameter.

Center, Diameter, Radius Relationships


O A

Chord - Segments with endpoints on the circle DE

D

E B

C

Arc - a part of a circle ex. AC - half of a Semic circlircle e BC

Anatomy of Circle - II


is the ratio of the circumference of any circle to its diameter. The circumference is approximately 3.14 (22/7) times bigger than the diameter.

O

B

C

CircumferenceCircumference - the “perimeter” of a circle - the distance

of one complete revolution

CircumferenceCircumference - the “perimeter” of a circle - the distance

of one complete revolution

14.37

22

Diameter

nceCircumfere

CD

1d 2d 3d .14d

C = D = 2r

Circumference & Pie (π)


Find the circumference of a circle, to the nearest tenth, if the diameter is 14.

C = D = 2RC = D = 2R

C = 3.14(14) = 43.96 44.0

C = (14) = 14C = (22/7)(14) = 44

Find the radius of a circle, to the nearest tenth, if the circumference is 63.

63 = 3.14(2R) 20.063694 = (2R)

20.063694 = (2R)

10.031847 = R 10.0

Model Problems


A manufacturer advertises that a new car has a turning radius of only 16.1 ft. The distance between the two front tires is 4.7 ft. How much farther must the outer wheel travel in making a complete circle than the tires on the inside?

Model Problem

16.1 ft.

11.4 ft.

Radius of inner circle?

16.1 ft. - 4.7 ft. = 11.4 ft.

C = D = 2RC = D = 2R

CO = π(2)(16.1)

CO = π(32.2)

CI = π(2)(11.4)

CI = π(22.8)

CO - CI =

32.222.8ft.

4.7 ft.

4.7 ft.


The diameter of a bicycle wheel is 26 in. To the nearest whole number, how many revolutions does the wheel make when the bicycle travels 100 yards.

1. Find the circumference of the wheel

C = π D = π 2RC = π D = π 2R

C = π26 = 3.14(26) = 81.64 in.

26”100 yds.

2. Find how many inches in 100 yds.

36 x 100 = 3600 inches

3. Divide inches traveled by circumference 3600 81.64 = 44.096031 44 revolutions

Model Problem


The Product Rule

Aim: What are properties of a Circle? Course: Applied Geo. In the figure above, two parallel lines...

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