(
o 1s c-ht' eel'\ tre Cf3 IS the t, A &Ol: IS Q
AS =oc. c ~ e11c 9,v o d
diometer
OA "08 erad u) C e.q_tJOI t , e q_lJOI
J\ .. cc onvtrs e t.~t
..-\
,. " 8
-'\
CL oPP = 5 1des)
B /I _;: qo c no r ds) C t. C ',:I CIIC. q.\J ad }
\ CL ,-,, Q sem1 -
\ C i, r c1e)
p,'( 1
A
.A
Ar 8 1s q t:on9ent;-
,'\ A
OM .L .A B
fj C 1.S
a 1ame~e.r
t he
fl
A+
,\
Q ,._ 0 "
C
..,
= 110°
,~o D ,,, ·CoTc 0n.L..A8r ci d, OS)J.
0 C C. • •
(IJl'>e f r om cen tre.
C conver .I e L. c opp L cl:} e 11c.
t;o rn1dp1: . Of chord) 1
8 ·1n o semi - qyod)
,Je, 6
...
A ilo;::_ 11 .'_. ' II c1 r t lt.)
;,.
..,-- ' ,._,__
' -e B
.ATS 1s q eo n9f! n t a t 't
A -' A 8C0 IS q c co nver s e t at') J.. ro d w .s)
.AM=MB ...
A• 0
"6::: C c13cuc qyo d
0
t11ne from ce.n t; r~
J. 1; 0 chord)
CL ,n sol""le
segment)
V .
\? (, Ccon\JC!r S e
6()('
c~ c 11c.
f.
q,uadJ
D
CA ancl BA ore
g i
t ton9~nt.s
A
,48 E = 8 c... C.A = C.8
o,
D
CO IS th e A ScD ,s q ce1- t: £ ct:a n s f ro,r, s cr rnc.
d,ornetev c~ c 11c. qyad c.~cl t C q_vad)
P.. pt . )
c.p e.rp b 1se.ceor o~ c co rwe r se £ "'
c hor d) 5qm e sc9nH !t"lt,)
A~B 13
\)
t,
D A0c ,s a ccn5ent
A A .... ;\ A A
f>. = D A : 0 or 8 = E
· ·ce·q,..,o'·c kor ds . t
,,. "
0=21' A " eqyoi .t.., c eo n c h ord c- h eo re n-i)
l J. o e- c ener e "
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A
\ -'\
•
/\
::::::--i , ¥-K
R
•
C
f =A A,.._ -
I( 11 ) c.. AS C IS q
c,q,0 0 1 c ir c le$ to
t; Qf"l 9 ent Q
e.q,1Jn' c ho r"ds , cir cle cl, a i..LJ ,,
eq,vol £.) eh ro u9 h 6J .P
Is p,,
c con ve.rs e. eon cho rd
t;he,o , ern)
\, • 1 ,, •O
/Jo
, i\, 'Vo
~ ~vf .s ...._,a ... ~- (.,
a/\n
~ S ~~- I . AAA e,o /1 A e
r 1.55':i / .. \ ,
tvo -B ' AC2t
• "' f
vc
z.~
,.. 1 " C. l£ SC. c..O
" 6 0 F cprop theorem
7. . 51d e $ o( 4
801/Af:)
B
1. . SAS 2p -z..t
,n p<0pon•o~ C.
.,. "- mvs c be
between A . !;j c. SD/IAf,
S ,des
.!iv-·
A c C ·
o,
." .~ .1A8l lll A OE f ·. -:J,;' ,:, '- 1v~e du.11cles
A f; 'l
sides
3 . SAA A,n prop)
J
"> ti"e s,cle
mv!.t be ,11
c..
the so,....e 80//AE ond
p0S1 t IOn In rel a t•On to Af : 2,.8D
t;he Sides fn both tr1on9ll!'S
B , C. m,dpt .
Ii- . RH5 A t t'heorem)
<..
6
, co:Of ond
f\ < ,D
At, iSD
.• AASc,: A D~f C.hl")e. ehrc,u9h
,,. e Nl II to
,cl p t .
se.c;on.d ~1de.)
L'S
C0
• •
,,eSP £ '5 ,..
r a,,e., _ c.o
o.lt '!
, ~s •s ,,., _,.-,t
e. • t .., '7ad 50 ,,.,e t pa\"'es l
t.•s~
opp ,,,,,
•••
C':fcllc -,,
_
1 /
C'UCIIC
, q_voo.l
st9me,.,
I 016
/
'3eo meer~__,..
. proput ise.
criangt
e
I '-o
. \ :.~ws
g C.
4 A8C. ll\ 4 oe·A Ill 4 OA c..
q eions l perp from nsht I. ve,ee1<
<GM poM' '!,•OS -....... . • onq" _ t;O h9p)
entV . J ·""cef'lt~r
- -•at
ton chord/J/ _
pt. . '\ 5e- I ' - - - - - I , - - -- I
.,,t on9 """ ,
chore!
theo,e.1n / .eqya•
an9 ieJ I AA8c.
1
II\ A 08A I AA8C 111 40Al. 1
I I
OBA Ill A0Al 1
A8z::08 · Bc.. ! Ac1. : co - c8 1 AD,. = SO · Oc. :
,__ - --- --~--------..L. ___ - - - - -.
,oo .I.,. d11JS 11
Of
0m
.
"''"'
1.•1
som• -
,n q
,,e f ' tO m1dpt • cir c,e
f''""
'
11rie rad11
cent-r e pup. chord dral'Y' e- tef
, PROPOP. TIONALTl TI-IEORlM ' C Prop, theorem , S tote parQlle•sJ
C.,ven : Ofl/8C
R~qy,red e-o prove ·. AD -: At
BD Et
con s t r uc t h e,9h t h r e Ia t, v e t o ba & e AO In
AAOE. (onSC:ruct: he19ht 'k' re1QtlV€ co l,C1se AE
'"' AADf. Jolt"\ a~ Ql°"\d l)C. t:O creoee 4QOf
and ACED .
A..-ea AAOE: 1,a11o•h
"
Area 4 8Df { · so· h _., ob 1:\ISC!. 4 has ..L he19he
-80
Q
(
r AP cuesule 0~ the cr•ari91e.
p..
AADE I
Areo : 1-·AE•k
Ar-ea E ,.
A 0(
1'tl•k
" AE .B
El
8ut:: A8Dt:: llOCE Csarne ba.se, .sanie he 1 9nt: and
''::J'"9 between para11e1 lines)
Area AAOE- Ateo 6.AOE, ar-ea Of AA OE , a; ter s1mp1 If 1cqc•or'l eci,oo• s
• • ::
bot~ AO Qr\d Af
Area A ~Dt Arec:i AOC~
. ", -8D
;AD
-
At
(.C.