bài tập nâng cao hình học lớp 10 học kỳ ii có đáp án

Chương   1  3   !"  ! " #$% &'()*%+,  ! &(/0+,12(.! &%+,345 ! 6))7 8 6/)/)745 #9: #;)<=)> ) #;)<=?)62))7 #+2,21@8 & A! 1@* 5B8CD)E 5B8CD)E) 5B8CD)5    #$%&'()#*+(,-./( '()#*+(0FGHIJB$ ,:8K&L4M ,:8N G B4M$E>B;<LG A2)B;)B%45 ,:8O&L:@=P2Q:RC -:)S #T(3B:*@@ #GH/'G<U:VWX%Y0+,1 /'I&L=@ ,G<U /:V/G #T(/:V/G*0+,1  #Z(/:V/G*0+,1  '()#*+(1"9:67[@ #9: @\%GHI] #/(G]BG2^/=:VR! :VRK_+2,?<GP48:V$ 1GK`M$E9: & #\ + , 1 T 1 , + ' + , 1T 1 ,Z + 1GN`M$E]BG 0+,C2  "Y:@:V+,!D)+,   2 + , C C  d :VRN_+2,?9P48:V$ Ta+b5B8+D)$ 0+C,2 !  T 2  234 #?9P?P48:V@ ^U! cY)_+2,?9P48:V$ cY)_+2,?P48:V$ @ :VRK_+2,?9P48:V$ :VRN_+2,?P48:V$ Ta+b(5B*+D)$2< !   '()#*+(5@@Y))> *(P,18 &(@Y)*+(P:V,1 _I=:@! #@+b5B8+D),1()++b '()#*+(6:G  :G :V:R4M$E\Y(%G! -%Ka= G@:G@;$% LU -%N-aGURY\)B%45;$%$@ :GI]=)D)L58G@GH(8]GH I]*G)B%45 + , C C  d +b '   + , C d C  + , C C  d +b   9 : 234 T])  L9::8 T])  L9: T])  L9::8 + +b _ , 1  3 '()#*+(7@D)dU ,:8K&(^@D)dU$aLY?);)<=@D) =!8!QB;)<= ,:8NMe=:@:R8%<L%*    e=;) <= ,:8OY()Q!f D)dU*C( 1L:VY)(Q C^:VPTY)( 234!   8=ET4)> 20+,1Y ( ) A 1;0 , ( ) B 3; 5 ,- -  ( ) C 0;3  1gFGHZ4 AE 2BC= uuur uuur  2gFGHh4 AF CF 5= =  3g@QRC4 ( ) 2 MA MB 3MC MB MC+ - = - uuur uuur uuur uuur uuur  #`!1g ( ) E 7;16 2g ( ) ( )  F 4;0 F 5;3- Ú 3g(:VW ( ) Tâm I 4; 19 Bk : R 73 ì ï - - ï ï í ï = ï ï î   )> 20+,1  ( ) ( ) ( ) A 4;1 ,B 2;4 ,C 2; 2- -  1g1B?+2,21<>6%G7 2gU · cosCBA  3gU)$=U0+,1UG<U:VWYG 4g@C4! 2MA 3MB MC 0+ - = uuur uuur uuur r  #`!1g · 5 cosCBA 5 = 2g ( )   ABC 6 Chu vi 6 5 1 ; S 5 1 D = + = + 3g ( ) M 1;4-   *8()-9:;23"<(9=>(?>1@@6A,B31C 8=ET4)> 2 ( ) A 2; 3 ,- -  ( ) B 2;1 , ( ) C 2; 1- @3TBG+,1T(@@ #`! ( ) D 2; 5- -   8=E)> 2 ( ) A 4;3 ,  ( ) B 2;7 ,  ( ) C 3; 8- -  1g@T4+,1T(@@  4 2g@'*:V+,1 3g@/2a/0+,1 4g@/:VW%Y0+,1 #`!1g ( ) D 1; 12- - 2g 4 1 I ; 9 3 æ ö ÷ ç ÷ - - ç ÷ ç ÷ ç è ø 3g ( )  2 G 1; , H 13;0 3 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø 4g ( ) J 5;1-   8=E)> 2 ( ) A 1;5 ,  ( ) B 4; 5 ,- -  ( ) C 4; 1- @ /:VWY0+,1 #`! ( ) I 1;0   '=:,=*:D()E(/=FGH:;=(:I1(?>0JJK 8=ET4)> 2@a/*0+,12 YG3 ( ) ( ) ( )  A 1;2 , B 5;7 , C 4; 3- -  #`! 1 21 H ; 11 11 æ ö ÷ ç ÷ - ç ÷ ç ÷ ç è ø   '=:,L:'>9M:3E#FGH:;=(:(?>1@@0 8=E)> 2 ( ) ( ) ( )  A 1;2 , B 2;0 , C 3;1- -  1gFGH/:VW%Y0+,1 2g@CP:V,14$=U0+,C? 1 3 $=U0+,1 #`!1g 11 13 I ; 14 4 æ ö ÷ ç ÷ - - ç ÷ ç ÷ ç è ø 2g   1 1 11 1 M ; M ; 3 3 3 3 æ ö æ ö ÷ ÷ ç ç ÷ ÷ Ú - ç ç ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø   '=:,N+,:9:*O =(?>1@@0 8=ET4)> 20+,1 3)i H ( ) C *45 1 y x = 1Ba/_*0+,1j) ( ) C  _T!& ( ) 1 1 1 A a; ,B b; ,C c; C a b c æ ö æ ö æ ö ÷ ÷ ÷ ç ç ç ÷ ÷ ÷ Î ç ç ç ÷ ÷ ÷ ç ç ç ÷ ÷ ÷ ç ç ç è ø è ø è ø f ( ) AH BC 1 H ; abc H C abc BH AC ì ï æ ö ^ ï ÷ ï ç ÷ Þ - - Þ Î ç í ÷ ç ÷ ï ç è ø ^ ï ï î uuur uuur uuur uuur   *8()L:'>9*>3>(?>1@@6 8=E ( ) ( ) A 1;2 , B 3;4- @1P :V d : x 2y 1 0- + = 40+,1)>%1 #`! ( )   3 4 C 3;2 C ; 5 5 æ ö ÷ ç ÷ Ú ç ÷ ç ÷ ç è ø  *8()D()):=<F(?>1@@6 8=ET4)> 20+,1)>%+8 ( ) B 3;0 ,-  ( ) C 7;0 , G<U:VWYG( r 2 10 5= - @/' *:VW%Y0+,12Y' )$: #`! ( ) ( )    I 2 10; 2 20 5 I 2 10; 2 10 5+ - Ú - -  '=:,PQ:R#(?>1@@0AB31C 8=Ea)k2 ( ) ( ) A 10;5 , B 15; 5 ,-  ( ) C 20;0- ( 3*@/+,1T@12Y?+,gg1T  5 #`! ( ) C 7; 26- -  '=:,23E#O =(?>0JJSAB31C 8=ET4)> 2@1):V x y 2 0- + = 40+,1)>%18 ( ) ( ) A 1; 2 , B 3;3- -  #`! ( )   7 3 C 1;3 C ; 2 2 æ ö ÷ ç ÷ Ú - - ç ÷ ç ÷ ç è ø  '=:,D()):=<FI0(?>0JJ7 1 ( ) A 1;1 P_J@,P:V y 3= 1PE40+,1(G;) #`!     4 5 4 5 B 1 ;3 , C 1 B 1 ;3 , C 1 3 3 3 3 æ ö æ ö æ ö æ ö ÷ ÷ ÷ ÷ ç ç ç ç ÷ ÷ ÷ ÷ - - Ú + + ç ç ç ç ÷ ÷ ÷ ÷ ç ç ç ç ÷ ÷ ÷ ÷ ç ç ç ç è ø è ø è ø è ø  '=:,T()UF(?>0JKV 8=ET4)> 2 ( ) A 1;0 ,-  ( ) B 1;0 (] $P:V d : y 1= _JU 2 2 MA MB @C4 ( )  MA k, k 0 MB = >  #`! 2 2 2 2 MA x 2x 2 MB x 2x 2 + + = - +  2 4 2 1;2 2 k 1 k 6k 1 M ;1 d k 1 æ ö ÷ + ± - + - ç ÷ ç Î ÷ ç ÷ ç ÷ - ÷ ç è ø  '=:,)*'=:-()(?>0JJ5 8=ET4)> 2 ( ) A 3cost; 0  ( ) B 0; 2sint @QRG ( ) o o M x ;y 4! 2AM 5MB 0+ = uuur uuur r <\ #`!QRC(( ( ) 2 2 x 9y E : 1 4 100 + =  '=:,PQ:R#(?>0JJJ 8=ET4)> 20+,1C]<l 1g1B?! u 3MA 5MB 2MC= - + r uuur uuur uuur <>E)HU*C 2g@QRCP4! 3MA 2MB 2MC MB MC+ - = - uuur uuur uuur uuur uuur  #`!1g u 2AC 5AB= - r uuur uuur 2g#:VW/ ( ) C /'2G<U CB R 3 =  ,=<()B(O()FGH:;=(:(?>1@@@ 8=ET4)> 20+,1 3 ( ) C 2; 4- -  / ( ) G 0;4  1g&L4M ( ) M 2;0 ()*%,1FGHG3+2, 2g&L4MC$P:V d : x y 2 0+ + = _J@D)dU,FGH C$%+,(m] #`!1g ( ) ( ) B 6;4 , A 4;12- 2/ n)dU( d : x y 2 0+ - = Ng 1 9 M ; 4 4 æ ö ÷ ç ÷ - ç ÷ ç ÷ ç è ø  '=:,)*'=:-()(?>1@@@  6 8=ET4)> 2( ( ) 2 P : y x=  :V d : y mx 1= + 1B?<\2:V()>()>m ( ( ) P %/=+,_J@D)dU/WW%Y0+,< \8(5 #`! ( ) ( )    1 1 2 2 A x ; mx 1 , B x ; mx 1+ + D)dU/(( ( ) 2 P ' : y 2x 1= +  '=,D()):=<F(?>0JJK  ( ) ( ) ( )  A 1;1 , B 3;3 , C 2;0  1gU$=Uo+,1 2g_J@]LGCPE4  · AMB I] #`! ( )  ABC S 2 .v.d.t D =  M Oº   ( ) ( ) ( )  A 1;3 , B 3;1 , C 2;4  gU$=Uo+,1 g@]LG M OxÎ 4  · AMB I] W;,:. I#3"X($=(:'=:,*8()IJK,B3 @PE4\G<LGfYG+,(I ] ( ) ( )  min hay PA PB+ ,Y?! 1g ( ) ( ) A 1;1 , B 2; 4-  2g ( ) ( ) A 1;2 , B 3;4  #`! g  g o o 6 5 1 P P ;0 . 2 P P ;0 5 3 æ ö æ ö ÷ ÷ ç ç ÷ ÷ º º ç ç ÷ ÷ ç ç ÷ ÷ ç ç è ø è ø  @P:V d : x y 0+ = C4\G<LGfCYG +,(I]G:VR4) 1g ( ) ( ) A 1;1 , B 2; 4- -  2g ( ) ( ) A 1;1 , B 3; 2-  1 ( ) M 4;1  ( ) ( ) A a;0 , B 0;b 8 a,b 0> 4+2,2C FGH+2,4 1gT=UG+,(I] ( ) OAB min S D  2g OA OB+ I] 3g 2 2 1 1 OA OB + I] #`!1g ( ) ( ) A 8;0 , B 0;2 2g ( ) ( ) A 6;0 , B 0;3 3g ( )  17 A ;0 , B 0;17 4 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø  1 ( ) M 2;1  ( ) ( ) A a;0 , B 0;b 8 a,b 0> 4+2,2C FGH+2,4! 1gT=UG+,(I] ( ) OAB min S D  2g OA OB+ I]  7 3g 2 2 1 1 OA OB + I] #`!1g ( ) ( ) A 4;0 , B 0;2  8=ET4)> 2 ( ) ( ) A 1; 2 , B 3;4-  1g@CPE4\<LGfCY+2,(m] 2g@cPE4 NA NB- ($] 3g@'PE)4 ( ) min IA IB+  4g@pPE)4 J A J B+ uur uur m] #`!1g 5 M ;0 3 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø 2g ( )   max NA NB 2 2 khi N 1;0- = -  3g ( )   min 1 IA IB 2 13 khi I 0; 2 æ ö ÷ ç ÷ + = - ç ÷ ç ÷ ç è ø  4g ( )   min J A J B 4khi J 0;1+ = uur uur  1 ( ) ( ) ( )  A 0;6 , B 2;5 , M 2t 2;t- @C4 1g ( ) min MA MB+  2g max MA MB-  1 ( ) ( ) ( )  A 1;2 , B 2;5 , M 2t 2;t+ @C4 1g ( ) min MA MB+  2g max MA MB+ uuur uuur  3g max MA MB-  4g min MA MB-  ,=<(9M:3E#E#Y(?>1@@@ 8=ET4)> 2@D)dUC4 <LGfCY ( ) A 1;2 <LGfCY()>?) *8()Z:%=[(?>1@@5 P2 ( ) ( ) A 1;2 , B 3;4 @P4  AP PB+ (I] #`! 5 P ;0 3 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø  '=:,\3%,=FGH:;=(:(?>0JJKA,B30C 8=E)> 2 ( ) ( )   2 A 0;2 , Parabol P : y x= FG HCP ( ) P 4 min AM  #`! 1;2 6 3 M ; 2 2 æ ö ÷ ç ÷ ç ± ÷ ç ÷ ç ÷ ç è ø   8   9 N]^]_ `,#-,:aF:-(),bc()#:8() ":R(de,#-,:aF:-()*:V∆Y)G* 44 980U=) cQ cY)("1*∆@j("1*∆ C:V:RGHY)Y"1 `,#-F:+F#3"f(,bc()#:8() ":R(de,#-F:+F#3"f(*:V∆Y)G* )> 8∆U =) cQ cY)("*∆@j("*∆ C:V:RGHY)Y" cY)("1("*∆@ :-()#Wg(:#:>$%,bc()#:8() 1:V∆D) :@45*6(457 cQ  &<(=45 *∆@ q8 q8 :-()#Wg(:,:;(:#h,,bc()#:8() 1:V∆D) :@Um* 0 u D r u D r 0 n D r r + 0 x y v  r + 0 x y v   :VR@:V<> :@Um  10 :-()#Wg(:#T()i3+#,bc()#:8() :@!862<>iV7:R(F:-()#Wg(:#T()i3+#*:V  cQ cY)∆ :@!@∆  cY)∆D) @:@*∆( #:V∆D):@*U,)=jOF:-()#Wg(:c()#:8() #:`**'(,:h(G #:V∆D) =45 <:@*U,)=jOF:-()#Wg(: c()#:8()#:`*:<$%)k,ZG C45:VR=! +,:<$%:-()#Wg(:c()#:8()∆;(:,:R#c()#:8()∆∆D)5% ∆gg∆≡∆gg∆≡Q#W;#-()%=,b:=c() #:8() 1:V %*∆ K ∆ N (=*=:@ # m= = =>= + 1 2 D º D Û = ( ) I >45= 1 1 1 x y 2 2 2 a b c D D D 0 a b c Û = = = Û = =  234!G)B345!   1 1 1 1 1 1 1 1 2 2 2 2 2 2 2 2 a b a b c a b c ; ; a b a b c a b c ¹ = ¹ = =  @ 2 2 2 a ,b ,c 0¹  [...]... 2004 Trong mt phng vi hờ truc toa ụ Descarter vuụng goc Oxy, cho ABC vuụng tai A vi B ( - 3;0) , C ( 7;0) , ban kinh ng tron nụi tiờp r = 2 10 - 5 Tim toa ụ tõm I cua ng tron nụi tiờp ABC, biờt iờm I co hoanh ụ dng ( ) ( S: I 2 + 10; 2 10 - 5 I 2 + ) 10; 2 10 - 5 Cao ng Tai Chinh K Toan nm 2004 Trong mt phng vi hờ truc toa ụ Oxy, cho ba iờm A ( 2;1) , B ( - 2;3) , C ( 4;5) Hay viờt phng trinh cac ng... ) 3 ù ù ợ Bai 83 Cao ng S Pham Ha Nụi khụi A nm 1999 Trong mt phng toa ụ Oxy, cho ABC, canh BC, cac ng cao BI, CK co phng trinh lõn lt la 7x + 5y - 8 = 0, 9x - 3y - 4 = 0, x + y - 2 = 0 Viờt phng trinh cac canh AB, AC va ng cao AH S: AB : x - y = 0, AC : x + 3y - 8 = 0, AH : 5x - 7y + 4 = 0 Bai 84 Cao ng Cụng Nghiờp Tp Hụ Chi Minh nm 2000 Trong mt phng toa ụ Oxy, cho ABC co cac ng cao ( BH) : x + y... viờt phng trinh ng thng BC S: BC : 4x + 3y + 4 = 0 + Cao ng Bn Tre nm 2005 Trong mt phng vi hờ truc toa ụ Oxy, viờt phng trinh cac canh cua ABC biờt inh A ( 4;- 1) , phng trinh mụt ng cao va mụt ng trung tuyờn ve cung mụt inh lõn lt la d1 : 2x - 3y + 12 = 0 va d2 : 2x + 3y = 0 S: AB : 3x + 7y - 5 = 0, AC : 3x + 2y - 10 = 0, BC : 9x + 11y + 5 = 0 + Cao ng Kinh T Ky Thuõt Cõn Th nm 2005 ;3 Trong mt phng... trinh ng cao BH : 2x - 3y - 10 = 0 va phng trinh ng thng BC : 5x - 3y - 34 = 0 Xac inh toa ụ cac inh B va C S: B ( 8;2) , C ( 5;- 3) + Cao ng S Pham Ha Nam khụi H nm 2005 Trong mt phng vi hờ truc toa ụ Descarter vuụng goc Oxy, cho A ( 1 ) , B ( - 5;4) va ng thng D : x + 3y - 2 = 0 Tim iờm M trờn ng ;2 uu uu ur ur D sao cho MA + MB ngn nhõt thng Page 27 ổ 5 3ử ữ ỗ S: M ỗ- ; ữ ỗ 2 2ữ ữ ố ứ + Cao ng... 1 ) , B ( 3;1) , C ( 4;3) Chng minh rng ABC la tam giac cõn Viờt phng ;2 trinh cac ng cao cua tam giac o S: AH : x + 2y - 5 = 0, BI : 3x + y - 10 = 0, CK : 2x - y - 5 = 0 + Cao ng Xõy Dng sụ 2 khụi A nm 2006 Trong mt phng vi hờ truc toa ụ Descarter vuụng goc Oxy, cho mụt tam giac co mụt inh la A ( 4;3) , mụt ng cao va mụt ng trung tuyờn i qua hai inh khac nhau co phng trinh lõn lt la 3x - y + 11 =... y + 29 = 0 + Cao ng Giao Thụng Võn Tai III Tp Hụ Chi Minh khụi A nm 2006 Trong mt phng vi hờ truc toa ụ Descarter vuụng goc Oxy, cho hinh thoi ABCD co phng trinh hai canh va mụt ng cheo la AB : 7x - 11y + 83 = 0, CD : 7x - 11y - 53 = 0 BD : 5x - 3y + 1 = 0 Tim toa ụ B va D Viờt phng , trinh ng cheo AC, rụi suy ra toa ụ cua A va C S: AC : 3x + 5y - 13 = 0 ị A ( - 4;5) , C ( 6;- 1) + Cao ng Ban Cụng... ( 8;- 7) + Cao ng Xõy Dng sụ 2 nm 2007 ;1 Viờt phng trinh cac canh cua ABC biờt inh A ( 1 ) , ng trung tuyờn va ng cao i qua inh B lõn lt co phng trinh: 3x + 4y - 27 = 0 2x + y - 8 = 0 , , S: AB : x = 1 AC : x - 2y + 1 = 0, BC : x + 8y - 49 = 0 + Cao ng Cụng Nghiờp Thc Phõm nm 2007 Trong mt phng vi hờ truc toa ụ Descarter vuụng goc Oxy, cho ABC co inh A ( 2 - 7) , trung tuyờn CM, ng cao BK co phng... C ỗ- ; ữ ữ ỗ 5 5ứ ữ ố Bai 87 Cao ng S Pham Vinh Phuc khụi A nm 2002 ;1 Trong mt phng toa ụ Oxy, cho ABC va iờm M ( - 1 ) la trung iờm cua AB Hai canh AC va BC theo th t nm trờn hai ng thng 2x + y - 2 = 0 va x + 3y - 3 = 0 1/ Xac inh toa ụ ba inh A, B, C cua ABC va viờt phng trinh ng cao CH 2/ Tinh diờn tich ABC ổ 4ử 3 ữ ;0 ỗ S: 1/ A ( 1 ) , B ( - 3;2) , C ỗ ; ữva CH : 10x - 5y - 2 = 0 ữ ỗ5 5ứ ữ ố... Mỗ ; ữ S: ỗ ỗ15 13ữ ữ ố ứ + Cao ng Truyờn Hỡnh khụi A nm 2005 ã Trong mt phng vi hờ truc toa ụ Oxy, cho ABC co AB = AC, BAC = 900 ổ ử 2 ; ỗ ữ Biờt M ( 1 - 1) la trung iờm canh BC va G ỗ ;0ữla trong tõm cua ABC Tim toa ữ ỗ3 ứ ố ữ ụ inh A, B, C + Cao ng Cụng ụng Vinh Long khụi A, B nm 2005 Trong mt phng vi hờ truc toa ụ Oxy, cho ABC co inh A ( 3;0) va phng trinh hai ng cao ( BB ') : 2x + 2y - 9 = 0... ( vdt) va AC : 16x + 13y - 68 = 0, 2 BC : 17x + 11y - 106 = 0 Bai 98 Cao ng khụi T M trng ai hoc Hung Vng nm 2004 Trong mt phng vi hờ truc toa ụ Descarter vuụng goc Oxy, cho ABC biờt inh A ( 3;9) va phng trinh cac ng trung tuyờn BM, CN lõn lt la : 3x - 4y + 9 = 0 va y - 6 = 0 Viờt phng trinh ng trung tuyờn AD S: AD : 3x + 2y - 27 = 0 Bai 99 Cao ng Cụng Nghiờp IV nm 2004 Trong mt phng vi hờ truc . , G<U:VWYG( r 2 10 5= - @/' *:VW%Y0+,12Y' )$: #`! ( ) ( )    I 2 10; 2 20 5 I 2 10; 2 10 5+ - Ú - -  '=:,PQ:R#(?>1@@0AB31C 8=Ea)k2 (. 4 , : 1 2 - + - D = -  8g ( )   x 2 y 3 A 4; 6 , : 3 10 + - - D = -  9g ( )  x 2t A 1;0 , : y 1 4t ì ï = ï D í ï = - ï î  10g ( )  x 2 t A 0;7 , : y t ì ï = - + ï D í ï = - ï î  . ;y 4! 2AM 5MB 0+ = uuur uuur r < #`!QRC(( ( ) 2 2 x 9y E : 1 4 100 + =  '=:,PQ:R#(?>0JJJ 8=ET4)>