topic 12(angle,arcs, segment & sector of circles)

8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)

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TOPIC 12

CIRCLES AND THEIRELEMENTS

Describe central angle and arcs of acircle

Sole sector of a circle !sing t"ecentral angles

and lengt" of arcs


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Arc Notation and Description

A minor arcis labeled with 2 capital letters which

are the endpoints and measures less than 180.

Major arcsand semicirclesare labeled with 3 letters

the endpoints and an !N" point in between.

#emicircle $ 180

Major arc is %reater than 180


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Degree Measures of Arcs

A central angleis formed by the intersection of 2segments at the center of a circle.

The endpoints of the segment that intersect the edge ofthe circle are the endpoints of the intercepted arc.


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Arcs can be measured in terms of

degrees.

The degree measure of a minor arcisthe measure of its central angle.

The degree measure of a major arcis36! minus the degree measure of itsminor arc. "#n this case the major arc

A$% &ould be 36!'()! * 2+)!,

The degree measure of a semicircleis-(!.

$
http://images.google.com/imgres?imgurl=http://www.regentsprep.org/Regents/math/geometry/GP15/ArcPic2.gif&imgrefurl=http://www.regentsprep.org/Regents/math/geometry/GP15/CircleArcs.htm&h=112&w=96&sz=3&hl=en&start=20&um=1&tbnid=i9GhWtvbJEXWFM:&tbnh=86&tbnw=74&prev=/images%3Fq%3Ddegree%2Bmeasures%2Bof%2Barcs%26svnum%3D10%26um%3D1%26hl%3Den%26rls%3DGGLG,GGLG:2005-44,GGLG:en%26sa%3DN


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Arc ength

A second &ay to measure an arc is in terms of its length. arc ength * the degree Measure of an arc "the circumference of the circle, 36!

* M "2/r,

36!

0ind the length of arc A% ifsegment A1 * - units.

* () "2 / -, * -.(3 in.

36

1


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ets 4ractice

Degree measure of arc A% *

Degree measure of arc $A *

Degree measure of arc %$ *

Degree measure of arc %A$ *

ength of arc A% *

+!

-3!

-6!

2!

3.66 units


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5#T7%8A9D:;;

Determine the length of an arc &ith the

gi r * 6

2. m 4 * +)!> r * 2

3. m 4 * (!> r * 3?

. m 4 * -3!> r * 6-

.-?

26.-(

).)

-3(.


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:egment and :ector of a

$ircle


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Segment of a circle is a part of a circle= bounded by the arc

A$% and the corresponding chord A% "0ig 2,. A length of the

perpendicular $D= dra&n from a midpoint of the chord A% until

intersecting &ith the arc A$%= is called a heightof a circle segment.

Sector of a circle is a part of a circle= bounded by the

arc Am% and t&o radii 8A and 8%= dra&n to the ends of the arc

" 0ig.3 ,.


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#ector o& a 'ircle#ector o& a 'ircle

(he re%ion bounded b 2 radii ) their(he re%ion bounded b 2 radii ) theirintercepted arc.intercepted arc.

#ector#ector

Also aAlso a

sectorsector

*isuall+ it mi%ht remind ou o& a slice*isuall+ it mi%ht remind ou o& a slice

o& pi,,a or a piece o& pie.o& pi,,a or a piece o& pie.


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(heorem(heorem Area o& a #ectorArea o& a #ector

2

360

r

measurearcA o =


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"-"- /ind the area o& the small sector /ind the area o& the small sector

shown.shown.

2

360

rmeasurearcAo

=

1313oo11m11m

( )2

11360

135= o

o

A

121

360

135=A

255.142 mA =


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"-"- ) M are 2 pts. on a circle with ) M are 2 pts. on a circle with

r$0 cm ) mr$0 cm ) m

M$10M$10oo. /ind the areas. /ind the areas

o& the sectors &ormed bo& the sectors &ormed b M.M.2

360

r

measurearcA

oI =

2

360

r

measurearcA

oII =

1010oo

II

IIII( ) 250360150 =IA

249.3272 cmAI =

( ) 250360

210=

IIA

249.4581 cmAII =

MM

0cm0cm


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"-"- /ind the area o& the shaded re%ion. /ind the area o& the shaded re%ion.

3cm3cm

regionshadedo AAA =

r24

32s

3cm3cm

3030oo22

22##33

##33

",2

-6

( )4

3342

4

3316 =

4

348= 312=

1414

5 125 12

##

33

$ 26. cm$ 26. cm22

topic 12(angle,arcs, segment & sector of circles)

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