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Bài tập hình học nâng cao 10 HK2

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5 ,- -  ( ) C 0;3  1hQR,S#,-,1%a AE 2BC= uuur uuur  2hQR,S#,-,1%i AF CF 5= =  3h%#Y,1%N ( ) 2 MA MB 3MC MB MC+ - = - uuur uuur uuur uuur uuur  e61h ( ) E 7;16 2h ( ) ( )  F 4;0 F 5;3- Ú 3h;,G]#)^ ( ) Tâm I 4; 19 Bk : R 73 ì ï - - ï ï í ï = ï ï î   )%*#+2<$5./0A@>5 ( ) ( ) ( ) A 4;1 ,B 2;4 ,C 2; 2- -  1hM%)K",1%>AAI$#+D#8#%-##%RE 2h\ · cosCBA  3h\<227J#\@>\"RI\,G]#)^-#`#%R 4h%,1%N6 2MA 3MB MC 0+ - = uuur uuur uuur r  e61h · 5 cosCBA 5 = 2h ( )   ABC 6 Chu vi 6 5 1 ; S 5 1 D = + = + 3h ( ) M 1;4-   '</2=>?78*@=ABCB6DD;E1F8$$$!6G )%*#+2FJ#)P#,-[()#()2<$5./0A",1% ( ) A 2; 3 ,- -  ( ) B 2;1 , ( ) C 2; 1- %#,-,B[,1#MR>[;"  !"!#$%&&&& '( 4 ./0H%O<j#\%-#,1%#)%*#+#,-./0 GF9;,1% #%O<j#\27f2V#`#2)K"<-,H<IJ,1#%O< J62F6#M,H<IJ GFW%kJG4#)#,GYF8IV80=/  *0  kJ2,H< IJ GFX`#;<6#l#5O<j#\=,1%N; V,G]`<;# N-# ,G]#)[`<; 7896    e6 ( ) D 2; 5- -   )%*#+2FJ#)P#,-2<$5./0A ( ) A 4;3 ,  ( ) B 2;7 ,  ( ) C 3; 8- -  1h%,1%[>[;" 2h%,1%:=,G]#+.>2 3h%#,-#)#%A#)f#%@> 4h%#%,G]#)^8#`@> e61h ( ) D 1; 12- - 2h 4 1 I ; 9 3 æ ö ÷ ç ÷ - - ç ÷ ç ÷ ç è ø 3h ( )  2 G 1; , H 13;0 3 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø 4h ( ) J 5;1-   )%*#+2FJ#)P#,-2<$5./0A ( ) A 1;5 ,  ( ) B 4; 5 ,- -  ( ) C 4; 1- % #%,G]#)^-#`@> e6 ( ) I 1;0   .A>&1A>I/"J4AK>?A>!L6CB5MMN )%*#+2FJ#)P#,-[()#()2<$5./0A#%#,-#)f#%=@>A "`##,-R,B ( ) ( ) ( )  A 1;2 , B 5;7 , C 4; 3- -  e6 1 21 H ; 11 11 æ ö ÷ ç ÷ - ç ÷ ç ÷ ç è ø   .A>&1O>.B=P>8JK>?A>CB6DD5 )%*#+2FJ#)P#,-2<$5./0A ( ) ( ) ( )  A 1;2 , B 2;0 , C 3;1- -  1hQR,S#%,G]#)^8#`@> 2h%,1%N#),G]#+7J#\@>N"K 1 3 7J#\@> e61h 11 13 I ; 14 4 æ ö ÷ ç ÷ - - ç ÷ ç ÷ ç è ø 2h   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   .A>&101>=>Q(ACB6DD5 )%*#+2FJ#)P#,-[()#()2<$5./0A@>5",B#<-,m #S ( ) C =%C 1 y x = M%#)f#%=@>n#<- ( ) C  [69 ( ) 1 1 1 A a; ,B b; ,C c; C a b c æ ö æ ö æ ö ÷ ÷ ÷ ç ç ç ÷ ÷ ÷ Î ç ç ç ÷ ÷ ÷ ç ç ç ÷ ÷ ÷ ç ç ç è ø è ø è ø l ( ) AH BC 1 H ; abc H C abc BH AC ì ï æ ö ^ ï ÷ ï ç ÷ Þ - - Þ Î ç í ÷ ç ÷ ï ç è ø ^ ï ï î uuur uuur uuur uuur   '</O>.B=B8BCB6DD; )%*#+2FJ#)P#,-./0,1% ( ) ( ) A 1;2 , B 3;4- %,1%#) ,G]#+ d : x 2y 1 0- + = @>2<$#8 e6 ( )   3 4 C 3;2 C ; 5 5 æ ö ÷ ç ÷ Ú ç ÷ ç ÷ ç è ø  '</I//>A@$"CB6DD; )%*#+2FJ#)P#,-[()#()2<$5./0A@>2<$#8>2F ( ) B 3;0 ,-  ( ) C 7;0 , "RI\,G]#)^-#`#%R; r 2 10 5= - %#,-#%: =,G]#)^8#`@>A"`#,1%:5#<,-7G4  !"!#$%&&&& '( 5    e6 ( ) ( )    I 2 10; 2 20 5 I 2 10; 2 10 5+ - Ú - -  .A>&1R!S>TCB6DD5EF8$"!6G )%*#+2FJ#)P#,-#)f<o./0A ( ) ( ) A 10;5 , B 15; 5 ,-  ( ) C 20;0- ;" ,B=%-##>[%#,-,1%A"`#)K>hh[ e6 ( ) C 7; 26- -  .A>&178JQ(ACB5MMUEF8$"!6G )%*#+2FJ#)P#,-[()#()2<$5./0A#%,1%#<-,G]#+ x y 2 0- + = @>2<$#82F ( ) ( ) A 1; 2 , B 3;3- -  e6 ( )   7 3 C 1;3 C ; 2 2 æ ö ÷ ç ÷ Ú - - ç ÷ ç ÷ ç è ø  .A>&1I//>A@$'L5CB5MMH ,1% ( ) A 1;1 #)%*#+#,-./0U0#%,1%#),G]#+ y 3= 2,1%#)#)P@>;#%R,H< e6     4 5 4 5 B 1 ;3 , C 1 B 1 ;3 , C 1 3 3 3 3 æ ö æ ö æ ö æ ö ÷ ÷ ÷ ÷ ç ç ç ç ÷ ÷ ÷ ÷ - - Ú + + ç ç ç ç ÷ ÷ ÷ ÷ ç ç ç ç ÷ ÷ ÷ ÷ ç ç ç ç è ø è ø è ø è ø  .A>&1V/WCB5MNX )%*#+2FJ#)P#,-[()#()2<$5./0A ( ) A 1;0 ,-  ( ) B 1;0 2;d0 ,1%7,-#),G]#+ d : y 1= U0#\ 2 2 MA MB 2#%N ( )  MA k, k 0 MB = >  e6 2 2 2 2 MA x 2x 2 MB x 2x 2 + + = - + 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  .A>&1/.A>2/CB5MM: )%*#+2FJ#)P#,-[()#()2<$5./0A,1% ( ) A 3cost; 0 2 ( ) B 0; 2sint %#YR,1% ( ) o o M x ;y 6 2AM 5MB 0+ = uuur uuur r I##0,c e6Y,1%N;(; ( ) 2 2 x 9y E : 1 4 100 + =  .A>&1RS>TCB5MMM )%*#+2FJ#)P#,-[()#()2<$5./0A@>2,1%N"d#Ip 1hM%)K6 u 3MA 5MB 2MC= - + r uuur uuur uuur I$P#<-22S#)\=,1%N 2h%#Y,1%N#)%*#+6 3MA 2MB 2MC MB MC+ - = - uuur uuur uuur uuur uuur  e61h u 2AC 5AB= - r uuur uuur 2hG]#)^#% ( ) C #%:A"RI\ CB R 3 =  &1"A@/FQ/K>?A>CB6DDD )%*#+2FJ#)P#,-[()#()2<$5./0A@>5,B ( ) C 2; 4- - 2 #)#% ( ) G 0;4  1h9VW ( ) M 2;0 ;#)<,1%=8QR,S#,-R,B>A  !"!#$%&&&& '( 6    2h9VWN7,-#),G]#+ d : x y 2 0+ + = U0#%O<j#\,1%QR,S N,1,-78>;qd# e61h ( ) ( ) B 6;4 , A 4;12- 2/ r<j#\; d : x y 2 0+ - = h 1 9 M ; 4 4 æ ö ÷ ç ÷ - ç ÷ ç ÷ ç è ø  .A>&1/.A>2/CB6DDD )%*#+2FJ#)P#,-[()#()2<$5./0A')"; ( ) 2 P : y x= 2 ,G]#+ d : y mx 1= + M%)KI%#0,cA,G]#+;<$;<$q# ')"; ( ) P #8,1%"J#>2U0#%O<j#\#%2^#)^8#`@.>I %#0,c2F.;C#,- e6 ( ) ( )    1 1 2 2 A x ; mx 1 , B x ; mx 1+ + 2O<j#\#%;')"; ( ) 2 P ' : y 2x 1= +  .A&1I//>A@CB5MMN )%*#+#,-./0",1% ( ) ( ) ( )  A 1;1 , B 3;3 , C 2;0  1h\7J#\s> 2hU0#%#d#VR,1%N#)#)P./5 · AMB Td# e6 ( ) , ABC S 2 .v.d.t D = 2 M Oº  )%*#+./0",1% ( ) ( ) ( )  A 1;3 , B 3;1 , C 2;4  h\7J#\s> "h%#d#VR,1% M OxÎ 5 · AMB Td# Y?1>3('L8*Z+A>.A>&1!'</!LMN!1F8" %#)#)P./,1%'#cRIVR#l',`R,1%>2;T d# ( ) ( )  min hay PA PB+ `#)K6 1h ( ) ( ) A 1;1 , B 2; 4-  2h ( ) ( ) A 1;2 , B 3;4  e6 h  h 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  %#),G]#+ d : x y 0+ = ,1%N#cRIVR#lN,`R ,1%>2;Td##)R#)G]Y< 1h ( ) ( ) A 1;1 , B 2; 4- -  2h ( ) ( ) A 1;1 , B 3; 2-  ,1% ( ) M 4;1 2,1% ( ) ( ) A a;0 , B 0;b 2F a,b 0> >AAN#+ QR,S#,-,1%>A 1h[J#\#%R.>;Td# ( ) OAB min S D  2h OA OB+ Td# 3h 2 2 1 1 OA OB + Td#  !"!#$%&&&& '( 7    e61h ( ) ( ) A 8;0 , B 0;2 2h ( ) ( ) A 6;0 , B 0;3 3h ( )  17 A ;0 , B 0;17 4 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø  ,1% ( ) M 2;1 2,1% ( ) ( ) A a;0 , B 0;b 2F a,b 0> >AAN#+ QR,S#,-,1%>A6 1h[J#\#%R.>;Td# ( ) OAB min S D  2h OA OB+ Td# 3h 2 2 1 1 OA OB + Td# e61h ( ) ( ) A 4;0 , B 0;2  )%*#+2FJ#)P#,-[()#()2<$5./0A ( ) ( ) A 1; 2 , B 3;4-  1h%,1%N#)#)P#cIVR#lN,`,1%>A;qd# 2h%,1%#)#)P NA NB- ;7d# 3h%,1%:#)#)P#< ( ) min IA IB+  4h%,1%t#)#)P#< J A J B+ uur uur qd# e61h 5 M ;0 3 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø 2h ( )   max NA NB 2 2 khi N 1;0- = -  3h ( )   min 1 IA IB 2 13 khi I 0; 2 æ ö ÷ ç ÷ + = - ç ÷ ç ÷ ç è ø  4h ( )   min J A J B 4 khi J 0;1+ = uur uur  ",1% ( ) ( ) ( )  A 0;6 , B 2;5 , M 2t 2;t- %#,-,1%N 1h ( ) min MA MB+  2h max MA MB-  ",1% ( ) ( ) ( )  A 1;2 , B 2;5 , M 2t 2;t+ %#,-,1%N 1h ( ) min MA MB+  2h max MA MB+ uuur uuur  3h max MA MB-  4h min MA MB-  &1"A@=P>8JJ[CB6DDD )%*#+2FJ#)P#,-[()#()2<$5./0A#%O<j#\,1%N IVR#lN,` ( ) A 1;2 2IVR#lN,`./;<$"K< '</\>,A]CB6DD: )%*#+./0A,1% ( ) ( ) A 1;2 , B 3;4 %#)#./%-#,1%'  AP PB+ ;Td# e6 5 P ;0 3 æ ö ÷ ç ÷ ç ÷ ç ÷ ç è ø  .A>&1^8,1AK>?A>CB5MMNE1F8$"!5G )%*#+2FJ#)P#,-2<$5./0A ( ) ( )   2 A 0;2 , Parabol P : y x= QR ,S,1%N#) ( ) P  min AM   !"!#$%&&&& '( 8    e6 1;2 6 3 M ; 2 2 æ ö ÷ ç ÷ ç ± ÷ ç ÷ ç ÷ ç è ø   !"!#$%&&&& '( 9      !"!#$%&&&& '( 10 !_`_a "121>b>2/1c'd/></ (#4,GY;ef121>b>2/=,G]#+∆`<R=5* #)!2F@\J< /3# `<;%-#'=∆#n;%-#'=∆ N-#,G]#+#,GY/R,S`<"`#%-#,1%2%-#' "12>08*g1c'd/></ (#4,GY;ef12>08*g=,G]#+∆`<R=52<$52F∆\ J< /3# `<;%-#'=∆#n;%-#'=∆ N-#,G]#+#,GY/R,S`<"`#%-#,1%2%-#' `<;%-#'2;%-#'=∆# >2/Yh>>B+,1c'd/></ ,G]#+∆,O<25'G4#)#%C=D;#%CE2 /3# 0 9I;JC5=∆# u2F u2F >2/Yh>1>?>i11c'd/></ ,G]#+∆,O<25'G4#)\#q= @ u D r u D r @ n D r v > @ x y v . v > @ x y v .  )#)G]Y*#,G]#+I$5G4#)\#q [...]... Vn on Trong mt phng vi hờ truc ta 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 Tỡm ta ụ tõm I cua ng tron nụi tiờp ABC, biờt iờm I co honh 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 ta ụ Oxy, cho ba iờm A ( 2;1) , B ( - 2;3) , C ( 4;5) Hay viờt phng trỡnh cac ng... 11y - 106 = 0 Bai 98 Cao ng khụi T M trng ai hoc Hung Vng nm 2004 Trong mt phng vi hờ truc ta ụ Descarter vuụng goc Oxy, cho ABC biờt inh A ( 3;9) v phng trỡnh cac ng trung tuyờn BM, CN lõn lt l : 3x - 4y + 9 = 0 v y - 6 = 0 Viờt phng trỡnh ng trung tuyờn AD S: AD : 3x + 2y - 27 = 0 Bai 99 Cao ng Cụng Nghiờp IV nm 2004 "Cõn cu bu thụng minh"WWW.ToanCapBa.Net Page 27 Bi Tp Nõng Cao Hỡnh Hc 10 HK... ( ) 3 ù ù ợ Bai 83 Cao ng S Pham Ha Nụi khụi A nm 1999 Trong mt phng ta ụ Oxy, cho ABC, canh BC, cac ng cao BI, CK co phng trỡnh lõn lt l 7x + 5y - 8 = 0, 9x - 3y - 4 = 0, x + y - 2 = 0 Viờt phng trỡnh cac canh AB, AC v 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 ta ụ Oxy, cho ABC co cac ng cao ( BH) : x + y -... = 0 + Cao ng Bn Tre nm 2005 Trong mt phng vi hờ truc ta ụ Oxy, viờt phng trỡnh cac canh cua ABC biờt inh A ( 4;- 1) , phng trỡnh mụt ng cao v mụt ng trung tuyờn ve cung mụt inh lõn lt l d1 : 2x - 3y + 12 = 0 v 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 "Cõn cu bu thụng minh"WWW.ToanCapBa.Net Page 28 Bi Tp Nõng Cao Hỡnh... ABC Tỡm ta ỗ ữ ữ ụ inh A, B, C + Cao ng Cụng ụng Vinh Long khụi A, B nm 2005 "Cõn cu bu thụng minh"WWW.ToanCapBa.Net Page 29 Bi Tp Nõng Cao Hỡnh Hc 10 HK 2 WWW.ToanCapBa.Net Ths Lờ Vn on Trong mt phng vi hờ truc ta ụ Oxy, cho ABC co inh A ( 3;0) v phng trỡnh hai ng cao ( BB ') : 2x + 2y - 9 = 0 v ( CC ') : 3x - 12y - 1 = 0 Viờt phng trỡnh cac canh cua tam giac ABC + Cao ng S Pham Ha Nụi khụi D1, T... minh"WWW.ToanCapBa.Net Page 30 Bi Tp Nõng Cao Hỡnh Hc 10 HK 2 WWW.ToanCapBa.Net Ths Lờ Vn on S: m = 1 m = 5 + Cao ng iờn Lc Tp Hụ Chi Minh nm 2006 Trong mt phng vi hờ truc ta ụ Descarter vuụng goc Oxy, cho ng thng d ;1 co phng trỡnh x + y - 3 = 0 v hai iờm A ( 1 ) , B ( - 3;4) Tỡm ta ụ iờm M thuục ng thng d sao cho khoang cach t M ờn ng thng AB bng 1 S: M ( 0;3) M ( 10; - 7) + Cao ng Kinh T Cụng Nghờ Tp Hụ... = 0 + Cao ng Kinh T ụi Ngoai nm 2007 Trong mt phng ta ụ Oxy, cho ABC Biờt iờm B ( 4;- 1) , ng cao AH co phng trỡnh l : 2x - 3y + 12 = 0, ng trung tuyờn AM co phng trỡnh "Cõn cu bu thụng minh"WWW.ToanCapBa.Net Page 31 Bi Tp Nõng Cao Hỡnh Hc 10 HK 2 WWW.ToanCapBa.Net Ths Lờ Vn on : 2x + 3y = 0 Viờt phng trỡnh cac ng thng cha cac canh cua tam giac ABC S: A ( - 3;2) , B ( 4;1) , C ( 8;- 7) + Cao ng... dõu cua tich nh sau: Dõu cua tich Phng trỡnh goc nhnPhng trỡnh goc tu Trong o: "Cõn cu bu thụng minh"WWW.ToanCapBa.Net Page 12 Bi Tp Nõng Cao Hỡnh Hc 10 HK 2 WWW.ToanCapBa.Net "Cõn cu bu thụng minh"WWW.ToanCapBa.Net Ths Lờ Vn on Page 13 Bi Tp Nõng Cao Hỡnh Hc 10 HK 2 WWW.ToanCapBa.Net Ths Lờ Vn on Dang toan 1 Lõp phng trỡnh ng thng va mụt sụ bai toan liờn quan Lõp phng trỡnh ng thng Lp phng trỡnh... Th nm 2005 "Cõn cu bu thụng minh"WWW.ToanCapBa.Net Page 28 Bi Tp Nõng Cao Hỡnh Hc 10 HK 2 WWW.ToanCapBa.Net Ths Lờ Vn on ;3 Trong mt phng vi hờ truc ta ụ Oxy, cho ABC co inh A ( 1 ) , phng trỡnh ng cao BH : 2x - 3y - 10 = 0 v phng trỡnh ng thng BC : 5x - 3y - 34 = 0 Xac inh ta ụ cac inh B v C S: B ( 8;2) , C ( 5;- 3) + Cao ng S Pham Ha Nam khụi H nm 2005 Trong mt phng vi hờ truc ta ụ Descarter vuụng... 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