angles et cercles - mathematique.org

!"#"$%&'(((((((()((((((((*+,-'.+,%/01(23.1(+44'1(((((((()((((((((5167%8(492(:(+4;<1&(1,(=18=<1&(
!
ANGLES'ET'CERCLES'
'
'
J’étudie':''''voir%cours%
'
! 5'>%4%,%74(?@04(+4;<1(+0(=14,81(?@04(=18=<1(
(
! 5'>%4%,%74(?@04(+4;<1(%4&=8%,(?+4&(04(=18=<1(
(
! A87B8%','&(?@04(+4;<1(+0(=14,81(%4,18=1B,+4,(<1(.C.1(+8=(/0@04(+4;<1(%4&=8%,(
(
! A87B8%','(?1(?10D(+4;<1&(%4&=8%,&(%4,18=1B,+4,(<1(.C.1(+8=(
(
(
J’applique':'
'
EF G74&,80%&(<@+4;<1(+0(=14,81(%4,18=1B,+4,(<1(.C.1(+8=(/01(<@+4;<1(%4&=8%,(81B8'&14,'"'
H4&0%,1I(47..1)<1(1,(=7.B<3,1(<@';+<%,'"'
'
(
DB
ˆ
C.2DA
ˆ
C=
((70((
2
DA
ˆ
C
DB
ˆ
C=
(
(
(
DC
ˆ
B.2DA
ˆ
B=
((70((
2
DA
ˆ
B
DC
ˆ
B=
(
(
DC
ˆ
B.2DA
ˆ
B=
((70((
2
DA
ˆ
B
DC
ˆ
B=
(
( ( (
((((((((
JF G74&,80%&(<@+4;<1(%4&=8%,(%4,18=1B,+4,(<1(.C.1(+8=(/01(<@+4;<1(+0(=14,81(81B8'&14,'"'
H4&0%,1I(47..1)<1(1,(=7.B<3,1(<@';+<%,'"'
'
(
BP
ˆ
C.2BA
ˆ
C=
((70((
2
DA
ˆ
C
BP
ˆ
C=
(
(
BP
ˆ
C.2BA
ˆ
C=
((70((
2
DA
ˆ
C
BP
ˆ
C=
(
(
(
BP
ˆ
C.2BA
ˆ
C=
((70((
2
DA
ˆ
C
BP
ˆ
C=
(

!"#"$%&'(((((((()((((((((*+,-'.+,%/01(23.1(+44'1(((((((()((((((((5167%8(492(:(+4;<1&(1,(=18=<1&(
(((
2F 5',18.%41(<1&(+.B<%,0?1&(K(1,(L(14(0,%<%&+4,(<1&(?744'1&(?0(?1&&%4(1,(M0&,%>%1(,1&(8'B74&1&(14(
'474N+4,(<1&(B87B8%','&(+?'/0+,1&"(
O0+4?(=@1&,(4'=1&&+%81I(47..1(<1&(+.B<%,0?1&(?1&(+4;<1&(B+8(?1&(<1,,81&(;81=/01&(PKI(LI(QI(RF(
B708(&%.B<%>%18(<1&(M0&,%>%=+,%74&((
(
(
(
(
(
K( S( TU9( =+8( ?+4&( 04( =18=<1I( ?10D( +4;<1&(
%4&=8%,&( /0%( %4,18=1B,14,( <1( .C.1( +8=( 74,( <+(
.C.1(+.B<%,0?1"(
L(S(EVU9(=+8(?+4&(04(=18=<1I(<@+.B<%,0?1(?@04(
+4;<1(+0(=14,81(6+0,(<1(?70W<1(?1(=1<<1(?@04(
+4;<1(%4&=8%,(%4,18=1B,+4,(<1(.C.1(+8="(
(
(
(
(
(
K( S( XV9( =+8( ?+4&( 04( =18=<1I( <@+.B<%,0?1( ?@04(
+4;<1( %4&=8%,( 6+0,( <+( .7%,%'( ?1( =1<<1( ?@04(
+4;<1(+0(=14,81(%4,18=1B,+4,(<1(.C.1(+8="(
(
(
(
(
L(S(EUU9(=+8(?+4&(04(=18=<1I(<@+.B<%,0?1(?@04(
+4;<1(+0(=14,81(6+0,(<1(?70W<1(?1(=1<<1(?@04(
+4;<1(%4&=8%,(%4,18=1B,+4,(<1(.C.1(+8="(
K(S(VU9(=+8(<1&(+4;<1&(Y(<+(W+&1(?@04(,8%+4;<1(
%&7=3<1(74,(<+(.C.1(+.B<%,0?1(1,(<+(&7..1(
?1&( +.B<%,0?1&( ?1&( +4;<1&( %4,'8%108&( ?@04(
,8%+4;<1(6+0,(,70M708&(EZU9"(
(
(
(
(
L( S( [T9( =+8( ?+4&( 04( =18=<1I( ?10D( +4;<1&(
%4&=8%,&( /0%( %4,18=1B,14,( <1( .C.1( +8=( 74,( <+(
.C.1(+.B<%,0?1"(
Q(S(\U9(=+8(,70,(,8%+4;<1(%4&=8%,(?+4&(04(?1.%)
=18=<1(1&,(81=,+4;<1"(
K( S( J29( =+8( <+( &7..1( ?1&( +.B<%,0?1&( ?1&(
+4;<1&(%4,'8%108&(?@04(,8%+4;<1(6+0,(,70M708&(
EZU9"(
(
(
(
(
L( S( 2Z9( =+8( ?+4&( 04( =18=<1I( <@+.B<%,0?1( ?@04(
+4;<1( %4&=8%,( 6+0,( <+( .7%,%'( ?1( =1<<1( ?@04(
+4;<1(+0(=14,81(%4,18=1B,+4,(<1(.C.1(+8="(
K( S( 2Z9( =+8( ?10D( ?87%,1&( B+8+<<3<1&( =70B'1&(
B+8( 041( ?87%,1( &'=+4,1( >78.14,( ?1&( +4;<1&(
+<,1841&)%4,1841&(?1(.C.1(+.B<%,0?1"(
(
(
(
(
(
L( S( E2[9( =+8( ?1&( +4;<1&( 7BB7&'&( B+8( <1(
&7..1,(74,(<+(.C.1(+.B<%,0?1"(
K(S( [Z9(=+8( ?+4&(04( =18=<1I(<@+.B<%,0?1( ?@04(
+4;<1( %4&=8%,( 6+0,( <+( .7%,%'( ?1( =1<<1( ?@04(
+4;<1(+0(=14,81(%4,18=1B,+4,(<1(.C.1(+8="(
(
L!
]G(//!ED!
Q!
L!
L!
L!