Gián án ÔN TẬP T 11 CỰC HAY

        . ' ' 'ABC A B C    = = = uuur r uuur r uuur r ' , ,AA a AB b AC c          !! "  #$  % uur AI $  #$  % r r r , ,a b c  &"  #$  % uuur AO $  #$  % r r r , ,a b c #%  '  "    &     !! "  #$  % uuur AG $  #$  % r r r , ,a b c #%      "   ∆ ' ' 'A B C  ()    * ( ) ( ) = + = + uuuur uuuur uuuuur uuur uuuuur 1 1 ' ' ' ' ' ' 2 2 MN AC A B AB A C #%  +,"  )%        --! !! $)    * ( ) = + + + uuur uuur uuur uuuur uuur 1 ' ' 4 AO AB AB AC AC  ( ) ( )           AI AB AC a b a c a b c = + = + + + = + + uur uuuur uuuur r r r r r r r ( ) ( ) ( ) ( ) ( )             AO AC AB a c b AO a c b AO AC AB a c b  = + = + +   ⇒ = + +   = + = + +   uuur uuuur uuur r r r uuur r r r uuur uuur uuuur r r r ( ) ( )              AG AA AB AC a a b a c a b c = + + = + + + + = + + uuur uuur uuuur uuuur r r r r r r r r      ( ) ( ) = + = + uuuur uuuur uuuuur uuur uuuuur 1 1 ' ' ' ' ' ' 2 2 MN AC A B AB A C           ! " # " $$%&%%' ( ( ) ( )                           AC A B AB A C AC A B AC A C AC AB A C A B B C B C + = + ⇔ + = + ⇔ − = − ⇔ = uuuur uuuuur uuuur uuuuur uuuur uuuuur uuuur uuuuur uuuur uuuur uuuuur uuuuur uuuuur uuuuur      ./-   - 0 a /-0/ 0/0/-/ /11  #1      )  "   ∆ ABC  )    * ⊥ ⊥ ,SA BC SB AC &)    * ( ) ⊥ SH ABC  2    ) 3 /-#    .  4- 5 )*+,- .#/$&-&0#1 2&32452 ⊥ &$6 ⊥ &45& ⊥ 2$ 07$ ⊥ 2& 0#1 SN BC BC SH AH BC ⊥  ⇒ ⊥  ⊥  895::'#:' 6;<=>0?@6ABB&C 0 c r a r b r 07$& ⊥ 26 80D#25 ( ) ⊥ SH ABC #'0E  :  # F 2$    @ " G$&H' 0#1 ( ) HS ABC ⊥ 45$6-I#J#/$2!G$&H 25:  # F 2$    @ " G$&H-1#K$6-2$ ( )    #:4    b AH b SAH a SA a = = =  L?5:#F2$@"G$&H8M  : 1α -1#4:#:  #:4  b a α = 67    ./- 8    9    "'   ( ) ⊥ SA ABCD /-0 · = ° 120BAD  2  :1       8#  / &        /)    * ( ) ⊥ OH ABCD  2  :1      / #  8 LI$&<-I:45 AC BD ⊥ ( ) SA ABCD ⊥ ⇒ $-I#J#/2!G$&<H 251#K#N8MOP P 80#1Q6- R8I#/S#2$456Q2$ - ( ) ( ) SA ABCD OH ABCD ⊥ ⇒ ⊥ #<$&451#K2&-<-1#K2&-$& 8MT P IS#2$&-S#U#V$                                         · = ° 30BAC  = = = = SA SB SC SD a    !"#  $ ( ) ⊥ SO ABCD  %&    ! '   () *  !+,   -    "!. /  /     !"#  $ ( ) ⊥ MN SBD  0&  1 /   ! '    LIQ-: .#/$-&<W2$32&3232<! ( ) SO AC SO ABCD SO BD ⊥  ⇒ ⊥  ⊥  80#1 ( ) SO ABCD ⊥ 45Q-I#J#/2!G$&<H 895::'#:' 6;<=>0?@6ABB&C 0 I · P PBCA = 45S#$<-S# X45   a CO = · ( ) · P  #:4 P  OC SCO SCO SC = = ⇒ = 'L?51#K2-G$&<H8MP P  #0#1 ( ) ( ) ( ) ( ) SO ABCD SO BD BD SO BD SAB DB AC BD SAB MN SAB MN AC ⊥ ⇒ ⊥ ⊥  ⇒ ⊥  ⊥  ⊥   ⇒ ⊥    P )*6-I#J#/Q!2& 0#1 ( ) AC SBD AC HO ⊥ ⇒ ⊥ 'Y:VZQ6- :V U1###/$-2& 0#1S#2Q&-S#U#VQ45Q63  a 2           ∆ ABC 3! -  45 67 !8549   · = ° 120BAC   -  !#  # /    = 3SA a *!:    !.     / .4   !"#  $ ( ) ⊥ AK SBC  %&    ! ' !#  # / $()  () &  1 /   ! '    0#1 ( ) SA ABC SA BC ⊥ ⇒ ⊥ 6$- R#:#/$&45 AH BC ⊥ ( ) ( ) ( ) AH BC BC SAH SA BC BC SAH BC AK AK SAH ⊥  ⇒ ⊥  ⊥  ⊥   ⇒ ⊥  ⊂   A-I#J#/$!2645 AK SH ⊥ ( ) AK SH BC AK AK SBC BC SH H ⊥   ⊥ ⇒ ⊥   ∩ =  8 ( ) ( ) ( ) ( ) ( ) ( ) · ( ) · ( ) ·    AH ACB SH SBC ABC SBC SH AH AHS SBC ABC BC SH AH BC ⊂   ⊂  ⇒ = =  ∩ =   ⊥  P   [P SA H H AH = = ⇒ = 895::'#:' 6;<=>0?@6ABB&C 0 0#1$6- :VU1###/2$-&?5\#K2$-&8M ;7    ./- 8    9- 8         · = ° 60BAD  = 3 2 a SA        /  .  4- 85  #%    "   ∆ ABD  )    * ( ) ⊥ BD SAC 2  // &   α       4/ 85#  4- 852   α tan 2  <    ) 3 8#  /- LI6-I#J#/2!G&<H4526 ⊥ &< $&<-I:45$ ⊥ &< ( ) SH BD AC BD BD SAC SH AC H ⊥   ⊥ ⇒ ⊥   ∩ =  $&<-I:#V-1# · P [PBAD = !S#$&<- S# X#V'   W [  a a OH OA OC = = =                        T '         T  T  T       a a a a a a SH SA AH AO SH a a a a SC SH HC AO a SC         = − = − = − = − =  ÷  ÷  ÷  ÷  ÷  ÷  ÷         ⇒ =   = + = + = +  ÷   ⇒ = 80#1 ( ) ( ) ( ) ( ) ( ) · ( )  T [  ' T   SAC BD SAC ABCD AC OH SO SAC SBD SO SH a HO a α α ⊥   ∩ = ⇒ =   ∩ =  = = = =7    ./-     9   ∆ ABC     > ( ) ⊥ SA ABC /-0          )    * ( ) ⊥ BC SAI &2  <    )  -    .  4/ 5 2    ) 3   .  4/ 5#  4- 5 0#1 ( ) SA ABC SA BC⊥ ⇒ ⊥ GH $&-S# XB- .#/&!$B ⊥ &GH 0DGH-GH45& ⊥ G2$BH 8)*6-I#J#/$!G2&H 0#1 895::'#:' 6;<=>0?@6ABB&C 0 ( ) ( ) ( ) ( ) SBC SAI H SI SBC SAI SI ⊥   ⇒ ∈  ∩   ]^S#U2$B#1              a AH AH AI SA AH a = + ⇒ = ⇒ = #0#1 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) · ( ) · ( ) ¶ ¶ ( ) ¶ P     P     BC SAI ABC ABC BC SBC ABC SI AI SIA SBC SAI SI ABC SAI AI SA a SIA SIA AI a ⊥   ∩ =  ⇒ = =  ∩ =   ∩ =  = = = ⇒ = ?@7    ./-  ( ) ⊥ SA ABC  ∆ ABC             /          -/#   = =2 3, 2SA a AB a  )    * ( ) ⊥ AH SBC  &2    ) 3   .  *4/ 5#  4- 5 2  <    ) 3 /-#    0#1 ( ) SA ABC SA BC⊥ ⇒ ⊥ GH $&-S# XB- .#/&!$B ⊥ &GH 0DGH-GH45& ⊥ G2$BH ( ) ( ) BC SAI SA AH AH SAI ⊥   ⇒ ⊥  ⊂    a 6  E  #!  # " $!2B! AH SI⊥ ( ) SA AH SI AH AH SBC SI BC I ⊥   ⊥ ⇒ ⊥   ∩ =  8 ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) · ( ) · ( ) ¶ ¶ ( ) ¶     W      BC SAI ABC ABC BC SA a SBC ABC SI AI SIA SIA SIA AI SBC SAI SI a ABC SAI AI α ⊥   ∩ =  ⇒ = = = = = ⇒ =  ∩ =   ∩ =  0: 1α-1#4:#: α3 #\: " #  # F 2$  &- _- :V$B3  a 895::'#:' 6;<=>0?@6ABB&C 0T ??*    ./-     9   ∆ ABC #1"#%  - 0 0 ( ) ⊥ SA ABC /-0        - )    * ( ) ⊥ BI SAC &2  :1      ) 3 >  .  4/-5#  4/ 5 2  <    ) 3 / #  - 895::'#:' 6;<=>0?@6ABB&C 0[ . 45Q-I#J#/2!G$&<H 895::'#:' 6;<=>0?@6ABB&C 0 I · P PBCA = 45S#$<-S#. tan 2  <    ) 3 8#  /- LI6-I#J#/2!G&<H4526 ⊥ &< $&<-I:45$