topic 12(angle,arcs, segment & sector of circles)
TRANSCRIPT
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
1/14
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
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
2/14
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
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
3/14
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.
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
4/14
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 -
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
5/14
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
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
6/14
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
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
7/14
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(.
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
8/14
:egment and :ector of a
$ircle
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
9/14
Segment of a circle is a part of a circle= bounded by the arc
A$% 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 ,.
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
10/14
#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.
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
11/14
(heorem(heorem Area o& a #ectorArea o& a #ector
2
360
r
measurearcA o =
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
12/14
"-"- /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 =
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
13/14
"-"- ) 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
-
8/10/2019 Topic 12(Angle,Arcs, Segment & Sector of Circles)
14/14
"-"- /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