etry ircles er 10 - Properties of Circles n 10.6 - Find Segment Lengths in Circles Geometry Chapter 10 - Properties of Circles Section 10.6 - Find Segment Lengths in Circles Geometry yhelines that intersect circles student shouldChapter get from 10 this: - Properties of Circles dtothe lengths of segments formed by lines that intersect solve problems Section 10.6 - Find Segment Lengthscircles in Circles e the lengths of segments in circles toshould solve problems What the student getGeometry from this: Chapter 10 - Properties of Circles . 1. Find the lengths of segments formed by lines that intersect circles Section 10.6 - Find Segment Lengths in Circles e need to know a couple of things... 2. Use the lengths of segments in circles to solve problems What the student should get from this: Geometry 1. Find the lengths of segments formed by lines that intersect intersect circles circles Whatofthe student should get from this: Chapter 10 - Properties Circles a tangent? First we need to know a couple of things... 2. Use the lengths of segments in circles toofsolve problems problems Find the lengths segments formed by lines that intersect circles Section 10.6 - Find1. Segment Lengths in Circles 2. Use the lengths of segments in circles to solve problems

a chord?

Whatʼs tangent? First wea need toWhat know a couple of things... First weget need to this: know a couple of things... the student should from

a secant?

2. Use the lengths Whatʼs of segments in circles to solve problems a tangent? Whatʼs Whatʼs aa chord? tangent?

each!

1. Find the lengths of segments formed by lines that intersect circles

First we need to know a couple of things... Whatʼs a chord?

Whatʼs Whatʼs aa secant? chord? Whatʼs a tangent? Whatʼs a chord? Whatʼs a secant? Draw each! Whatʼs a secant?

Whatʼs a secant?

Draw each!

Draw each! Draw each! ext thing to think about... ! ! ! !!!!!!! !!!!!!!!!!!!!!!! ! ! The next thing to think about... Last rule...ofwhen secant of intersects a tangent a circle, the square of the tangent chords the product their segments areofequal. The next thing tolengths think about... engthsintersect, of their segments arethe equal. If two chords intersect, the product of the lengths of their segments are equal. segment equals the product of the lengths of the other secant segment and its external The next thing to think about... Example: ple: Ifsegment. twonext chords intersect, the product of theoflengths their segments are equal. The thing toIf two think about... chords intersect, the product the lengthsof of their segments are equal. ! Example: Example: Example: If two chords segments ! intersect, the product of the lengths of their segments are are equal. equal. c a

c Example: a

a

a

a

b

a

b

c

b

c b

d

c d

Another example:

b

d d

Another example:

b c Another example: a !b = c ! d ! x

"#$%!&! d

Another example:

x

4.2

Another example: 2.5

2

2

x

x

4.2

! Another ! example: !2 !

2

2.5

!

!

4.2

Another Another example: example:

2.5

x

!

2xx 22

15

4.2 4.2 4.2 2.5 2.5 2.5

4.2 2.5

o secants intersect outside the circle, the product of the lengths and its external secant equals the intersects product of athe Last segment rule... when secant tangent of a circle, the square of the tangent ant segment and itssegment externalequals segment. the product of the lengths of the other secant segment and its external segment.

!

b

Another rule... when two secants intersect outside the circle, the product of the lengths Example: a of one secant segment and its external secant segment equals the product of the Last rule... when secant intersects a tangent of a circle, the square of the tangent lengths of the othertwo secant segment and its external segment. Another rule... when secants intersect outside the circle, productand of the lengths segment equals the product of the lengths of the other secantthe segment its external of oneExample: secant segment and its external secant segment equals the product of the a segment. rule... when two secants intersect outside and the circle, product of the lengths lengthsAnother of the other secant segment itstheexternal segment. of one secant segment and its external secant segment equals the product of the b a ! lengths of the othercsecant segment and its external segment. Example: ! Example: Example:

b

b

b

a

d

a

c

a

c

cd

c

d

b

a !(a + b) = c !(c + d) !

c d

! !

Another example:

Another example:

Another example: "#$%!&!

5

18

Another example: 18

5

18

5

16

x

16

16

x

Another example: 15

x

Another example:

when secant intersects a tangent18 of a circle, the square of the ! Last rule... ! ! ! ! 5 tangent Last rule... when secant intersects a tangent of a circle, the square of the tangent Last rule...equals when secant intersects a tangent circle, square of the tangent segment the product of the lengths of athe otherthe secant segment and its external segment equals the product of the lengths of the other secant segment and its external segment equals the product of the lengths of the other secant segment and its external 12 segment. segment. segment. 15 16 ! Example: x Example: ! Example: a

12

x

a

b

a

c

xbb

cc

! ! Another example: ! 15

12

! a2 = b ! (b + c ) !

c

Example: for the variables. Example: solve for thesolve variables. '(!

Another example:

!

15

12

variables.

Example: solve for the variables.

x

x

x

)(!!

3.5 in.

! 3.5 in.

Example: solve for the variables.

2.5 in.

2.5 in. x

3.5 in. 2.5 in.

x

x

3.5 in. 2.5 in.

.5 in.

x

x

x

!!!!!! *(!

! x 13.5 in.

13.5 in.

13.53.5 in.in.

13.5 in.

12 in.

x

x

x

2.5 in. 12 12 in.

12 in.

in.

Find the radius of the circle.

Find the radius of the circle.

Find the radius of the circle. Find the radius of the circle.

22 in.

n.

x

13.5 in.

22 in.

22 in.

2 in.

x

12 in.

!

3 in.

Find the radius of the circle. 12 in.

! 22 in.

3 in.

Find the radius of the circle. 12 in.

3 in.

3 in.

Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.

12 in.

3 in.

12 in. 3 in. ! !

!

12 in. ! ! ! ! ! ! !!! ! Assignment: p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next Assignment:period. p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next ! period. 12Assignment: in. p.692 #s 3-20 all, 22. Show work. Draw all pictures. Enjoy! Due next period.

Show work. Draw all pictures. Enjoy! Due next

1.

+,-.!/-012#1.3! 1.

March 29, 2012 ! 2.

March 29, 2012

2.

! 3.3.

! 4.

4.

!

/Geo1._Section_10.6

Published on May 20, 2012

http://www.houstonchristian.org/data/files/news/ClassLinks/Geo1._Section_10.6.pdf

Advertisement