10.1 Circles and Circumference
-
Upload
cora-schroeder -
Category
Documents
-
view
65 -
download
6
description
Transcript of 10.1 Circles and Circumference
![Page 1: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/1.jpg)
10.1 Circles and Circumference10.1 Circles and Circumference
![Page 2: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/2.jpg)
ObjectivesObjectives
Identify and use parts of circlesIdentify and use parts of circles
Solve problems using the Solve problems using the circumference of circlescircumference of circles
![Page 3: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/3.jpg)
Parts of CirclesParts of Circles
Circle Circle – set of all – set of all points in a plane points in a plane that are that are equidistant equidistant from a given point from a given point called the called the centercenter of of the circle.the circle.
A circle with center A circle with center P is called “circle P” P is called “circle P” or or PP..
P
![Page 4: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/4.jpg)
Parts of CirclesParts of Circles
The distance from the The distance from the center to a point on the center to a point on the circle is called the circle is called the radiusradius of the circle. of the circle.
The distance across the The distance across the circle through its center is circle through its center is the the diameter diameter of the of the circle. The diameter is circle. The diameter is twice the radius twice the radius d = 2rd = 2r or or r = ½ dr = ½ d).).
The terms The terms radius radius and and diameterdiameter describe describe segments as well as segments as well as measures.measures.
center
diameter
radius
![Page 5: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/5.jpg)
Parts of CirclesParts of Circles
QPQP , , QSQS , and , and QRQR are radii. are radii. All radii for the same circle All radii for the same circle
are congruent.are congruent. PRPR is a is a diameterdiameter.. All diameters for the same All diameters for the same
circle are congruent.circle are congruent. A A chordchord is a segment is a segment
whose endpoints are whose endpoints are points on the circle. points on the circle. PSPS and and PRPR are chords. are chords.
A diameter is a chord that A diameter is a chord that passes through the center passes through the center of the circle.of the circle.
P
Q
R
S
![Page 6: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/6.jpg)
Name the circle.
Answer: The circle has its center at E, so it is named circle E, or .
Example 1a:Example 1a:
![Page 7: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/7.jpg)
Answer: Four radii are shown: .
Name the radius of the circle.
Example 1b:Example 1b:
![Page 8: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/8.jpg)
Answer: Four chords are shown: .
Name a chord of the circle.
Example 1c:Example 1c:
![Page 9: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/9.jpg)
Name a diameter of the circle.
Answer: are the only chords that go through the center. So, are diameters.
Example 1d:Example 1d:
![Page 10: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/10.jpg)
Answer:
Answer:
a. Name the circle.
b. Name a radius of the circle.
c. Name a chord of the circle.
d. Name a diameter of the circle.
Answer:
Answer:
Your Turn:Your Turn:
![Page 11: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/11.jpg)
Answer: 9
Formula for radius
Substitute and simplify.
If ST 18, find RS.
Circle R has diameters and .
Example 2a:Example 2a:
![Page 12: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/12.jpg)
Answer: 48
Formula for diameter
Substitute and simplify.
If RM 24, find QM.
Circle R has diameters .
Example 2b:Example 2b:
![Page 13: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/13.jpg)
Answer: So, RP = 2.
Since all radii are congruent, RN = RP.
If RN 2, find RP.
Circle R has diameters .
Example 2c:Example 2c:
![Page 14: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/14.jpg)
Answer: 58
Answer: 12.5
a. If BG = 25, find MG.
b. If DM = 29, find DN.
Circle M has diameters
c. If MF = 8.5, find MG.
Answer: 8.5
Your Turn:Your Turn:
![Page 15: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/15.jpg)
Find EZ.
The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively.
Example 3a:Example 3a:
![Page 16: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/16.jpg)
Since the diameter of FZ = 5.
Since the diameter of , EF = 22.
Segment Addition Postulate
Substitution
is part of .
Simplify.
Answer: 27 mm
Example 3a:Example 3a:
![Page 17: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/17.jpg)
Find XF.
The diameters of and are 22 millimeters, 16 millimeters, and 10 millimeters, respectively.
Example 3b:Example 3b:
![Page 18: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/18.jpg)
Since the diameter of , EF = 22.
Answer: 11 mm
is part of . Since is a radius of
Example 3b:Example 3b:
![Page 19: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/19.jpg)
The diameters of , and are 5 inches, 9 inches, and 18 inches respectively.
a. Find AC.
b. Find EB.
Answer: 6.5 in.
Answer: 13.5 in.
Your Turn:Your Turn:
![Page 20: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/20.jpg)
CircumferenceCircumference
The The circumference circumference of a circle is of a circle is the distance around the circle. In the distance around the circle. In a circle, a circle,
C = 2C = 2ππr or r or ππdd
![Page 21: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/21.jpg)
Find C if r = 13 inches.
Circumference formula
Substitution
Answer:
Example 4a:Example 4a:
![Page 22: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/22.jpg)
Find C if d = 6 millimeters.
Circumference formula
Substitution
Answer:
Example 4b:Example 4b:
![Page 23: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/23.jpg)
Find d and r to the nearest hundredth if C = 65.4 feet.
Circumference formula
Substitution
Use a calculator.
Divide each side by .
Example 4c:Example 4c:
![Page 24: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/24.jpg)
Radius formula
Use a calculator.
Answer:
Example 4c:Example 4c:
![Page 25: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/25.jpg)
a. Find C if r = 22 centimeters.
b. Find C if d = 3 feet.
c. Find d and r to the nearest hundredth if C = 16.8 meters.
Answer:
Answer:
Answer:
Your Turn:Your Turn:
![Page 26: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/26.jpg)
Read the Test ItemYou are given a figure that involves a right triangle and a circle. You are asked to find the exact circumference of the circle.
MULTIPLE- CHOICE TEST ITEM Find the exact circumference of .
A B C D
Example 5:Example 5:
![Page 27: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/27.jpg)
Solve the Test ItemThe radius of the circle is the same length as either leg of the triangle. The legs of the triangle have equal length. Call the length x.
Pythagorean Theorem
Substitution
Divide each side by 2.
Simplify.
Take the square root of each side.
Example 5:Example 5:
![Page 28: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/28.jpg)
So the radius of the circle is 3.
Circumference formula
Substitution
Because we want the exact circumference, the answer is B.
Answer: B
Example 5:Example 5:
![Page 29: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/29.jpg)
Answer: C
Find the exact circumference of .
A B C D
Your Turn:Your Turn:
![Page 30: 10.1 Circles and Circumference](https://reader033.fdocuments.us/reader033/viewer/2022061603/5681329c550346895d99388e/html5/thumbnails/30.jpg)
AssignmentAssignment
GeometryGeometryPg. 526 #16 – 42, 44 – 54 Pg. 526 #16 – 42, 44 – 54
evensevens
Pre-AP Geometry Pre-AP Geometry Pg. 526 #16 - 56Pg. 526 #16 - 56