8/2/2019 Obj. 27 Circles (Presentation)
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B`c$ 0> Hgphemx
]dg| > Hbdghx
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Hbdhmy|x odl B`cmh|gqmx
Hgphemx &B`c$ (0>'
Glmd|gaw |fm m}o|gbd ba o hgphem$ ^pg|m |fm m}o|gbd ba o hgphem% ngqmd |fm hmd|mp odl
|fm polg}x$
]xm |fm hbjyem|gdn |fm x}opm jm|fbl |b lm|mpjgdm|fm hmd|mp odl polg}x ba o hgphem$
^pg|m |fm m}o|gbd ba o hgphem% ngqmd |fm hmd|mp odl o
ybgd| bd |fm hgphem$
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Hgphemx
\fm nmbjm|pgh lmagdg|gbd ba o hgphem gx |fm xm| ba oee
ybgd|x gd o yeodm |fo| egm o ngqmd lgx|odhm apbj o ngqmdybgd|$
^m hod }xm |fm lgx|odhm abpj}eo |b agdl |fm lgx|odhm
`m|~mmd |fm hmd|mp odl o ybgd|3
f
k&f% k'
&v%w'& ' & ' + :0 0
0 ? 0 ?v v w w p
p
& ' & ' + :
0 0
v f w k p
& ' & ' + :0 0 0v f w k p
8/2/2019 Obj. 27 Circles (Presentation)
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Hgphemx
Mvojyem3 ^pg|m |fm m}o|gbd ba o hgphem ~g|f g|x hmd|mp o|
&?% 0' odl polg}x 8$
Em|f : ?% k: 0% odl p: 8$ \fmpmabpm% |fm m}o|gbd abp
|fm hgphem gx
& ' & '& '00 0
? 0 8v w + :
& ' & ' + + :0 0
? 0 7v w
8/2/2019 Obj. 27 Circles (Presentation)
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Npoyfgdn Hgphemx
\b npoyf o hgphem bd npoyf yoymp% yeb| |fm hmd|mp ybgd|
odl hb}d| b}| |fm polg}x$ Bymd |fm hbjyoxx |b |fo|ybgd| odl lpo~ |fm hgphem$
Mvojyem3 Npoyf
Hmd|mp3 &8%
8/2/2019 Obj. 27 Circles (Presentation)
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Npoyfgdn Hgphemx
\b npoyf |fm hgphem bd wb}p hoeh}eo|bp% wb} ~gee dmml |b
xbeqm abpw3
Npoyf
Wb} ~gee dmml |b npoyf `b|f ye}x odl jgd}x qmpxgbdx gd
bplmp |b npoyf |fm a}ee hgphem$
& ' & ' + :0 0
8 < 7v w
& ' & ' : 0 0
< 7 8w v
& ' : 0
< 7 8w v
& ': +0
7 8
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Npoyfgdn Hgphemx
Md|mp
Md|mp
Hfodnm |fmq xm||gdn |b x}opm
\fm hoeh}eo|bp jow xfb~ o noy% `}||fo|x bkow$
& ': +0
7 8
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Nmdmpoe Abpj ba o Hgphem
\b nm| apbj |fm nmdmpoe m}o|gbd `ohk |b |fm hmd|mp*
polg}x abpj &xb ~m hod kdb~ |fm hmd|mp odl |fm polg}x'%~m hbjyem|m |fm x}opm abp `b|fvodlw$
Mvojyem3 ^fo| gx |fm hmd|mp odl polg}x ba |fm hgphem
~fbxm m}o|gbd gx
+ + :0 0
< 6
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Nmdmpoe Abpj ba o Hgphem
Mvojyem3 ^fo| gx |fm hmd|mp odl polg}x ba |fm hgphem
~fbxm m}o|gbd gx
\fm hmd|mp gx o|&0%
8/2/2019 Obj. 27 Circles (Presentation)
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Nmdmpoe Abpj ba o Hgphem
Mvojyem3 ^fo| gx |fm hmd|mp odl polg}x ba |fm hgphem
~fbxm m}o|gbd gx+ + :
0 00 0 0 1
8/2/2019 Obj. 27 Circles (Presentation)
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Nmdmpoe Abpj ba o Hgphem
Mvojyem &hbd|$'3
\fm hmd|mp gx o| % odl |fm polg}x gx =$
+ + :
0 0? 8
0 0 =90 0
v w
+ + :
0 0
? 8 0=0 0
v w
Lgqglm |fpb}nf
`w 0$
? 8
%0 0
8/2/2019 Obj. 27 Circles (Presentation)
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Hfopoh|mpgx|ghx bap0
^fmd ~m hbdqmp| apbj |fm nmdmpoe abpj |b |fm hmd|mp*
polg}x abpj% |fm hbdx|od| bd |fm pgnf|*fodl xglm |meex }xxbjm `oxgh gdabpjo|gbd$
Gap0 gx 4 9 &ybxg|gqm'% |fm npoyf ba |fm m}o|gbd gx o
hgphem ~g|f polg}x p$
Gap0 gx m}oe |b 9% |fm npoyf ba |fm m}o|gbd gx o xgdnem
ybgd|&f% k'$
Gap0 gx 5 9 &dmno|gqm'% |fmd db pmoe ybgd|x ~gee xo|gxaw
|fm m}o|gbd% odl o npoyf lbmx db| mvgx|$
8/2/2019 Obj. 27 Circles (Presentation)
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Hfopoh|mpgx|ghx
Mvojyem3 \fm npoyf ba |fm m}o|gbd
gx mg|fmp o ybgd| bp gx dbdmvgx|md|$ ^fghf gx g|2
Xgdhm p0 gx dmno|gqm% |fm npoyf gx dbdmvgx|md|$
+ + + :0 0
6 0 0< 9v w v w
& ' & '0 0 0 06 < 0 ? 0< ?1 ?v v w w + + + + : + +
& ' & ' + + + + : 0 0 0 06 < 0 ? >v v w w
& ' & ' + + : 0 0
< ? >v w
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^pg|gdn |fm M}o|gbd ba o Hgphem^m hod db~ |mee |fo| |fm m}o|gbd
gx o hgphem ~g|f o hmd|mp o|&0% 8' odl o polg}x ba
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^pg|gdn |fm M}o|gbd ba o Hgphem ^m hod }xm |fgx glmo |b ~pg|m |fm m}o|gbd ba o hgphem
ngqmd |fm hmd|mp odl o ybgd| bd |fm hgphem$
Mvojyem3 ^pg|m |fm m}o|gbd ba |fm hgphem ~g|f hmd|mp o|
&
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^pg|gdn |fm M}o|gbd ba o Hgphem Mvojyem3 ^pg|m |fm m}o|gbd ba |fm hgphem ~g|f hmd|mp o|
&
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Hgph}eop Gdm}oeg|gmx Hgph}eop gdm}oeg|gmx opm aogpew x|pognf|abp~opl$ Abp |fm
hmd|mp*polg}x abpj ba |fm hgphem% |fm npoyf ~gee `m \fm pmngbd gdxglm |fm hgphem ga |fm xwj`be gx 5 bp
\fm pmngbd b}|xglm |fm hgphem ga |fm xwj`be gx 4 bp
Ox ~g|f egdmx% 5 bp 4 gx npoyfml ~g|f o lb||ml egdm odl bp gx npoyfml ~g|f o xbegl egdm$
5
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Fbjm~bpk Hbeemnm Oenm`po
Yonm ?773 0?*89 &8x'%