Obj. 27 Circles (Presentation)

8/2/2019 Obj. 27 Circles (Presentation)

1/18

B`c$ 0> Hgphemx

]dg| > Hbdghx


2/18

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$


3/18

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


4/18

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


5/18

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%


6/18

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


7/18

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


8/18

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


9/18



~fbxm m}o|gbd gx

\fm hmd|mp gx o|&0%


10/18



~fbxm m}o|gbd gx+ + :

0 00 0 0 1


11/18


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


12/18

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|$


13/18

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


14/18

^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


15/18

^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|

&


16/18

^pg|gdn |fm M}o|gbd ba o Hgphem Mvojyem3 ^pg|m |fm m}o|gbd ba |fm hgphem ~g|f hmd|mp o|

&


17/18

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


18/18

Fbjm~bpk Hbeemnm Oenm`po

Yonm ?773 0?*89 &8x'%

Obj. 27 Circles (Presentation)

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