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Trang 169###################M T S � � �� THI V O THPT PH N BANI, Ph n 1 : C c � � � � �� thi v o ban�
c b n� � �� s 1C u 1 ( 3 i m ) � � � � Cho bi u th c : � � # EMBED Equation.3
� � Cho hai # ng tr n (O1) v (O2) c b n k nh b ng R c t nhau t i A � � � � � � � � � �
v B , qua A v c t tuy n c t hai # ng tr n (O1) v (O2) th t t i E v F , � � � � � � � � � � � � �
# ng th ng EC , DF c t nhau t i P Ch ng minh r ng : BE = BF M t c t tuy n
qua A v vu ng g c v i AB c t (O1) v (O2) l n l# t t i C,D Ch ng minh t � � � � � � � � � � �
gi c BEPF , BCPD n i ti p v BP vu ng g c v i EF T nh di n t ch ph n giao nhau � � � � � � � � � � �
v ON l ph n gi c c a g c ANB Ch ng minh M n m tr n m t cung tr n c � � � � � � � � � � � � ��nh khi
M thay ��i X c � ��nh v tr c a M � � � �� kho ng c ch O1O2 l ng n nh t � � � � � �� s 4 C u� �
1 ( 3 i m ) � � Cho bi u th c : # EMBED Equation.3 ###R t g n bi u th c T nh � � � � � � �
gi tr c a # EMBED Equation.3 ### khi # EMBED Equation.3 ###C u 2 ( 2 i m ) � � � � � �
Gi i ph# ng tr nh : # EMBED Equation.3 ###C u 3 ( 2 i m ) � � � � � � Cho h m �
s : y = -# EMBED Equation.3 ###T m x bi t f(x) = - 8 ; - # EMBED Equation.3 � � �
### ; 0 ; 2 Vi t ph# ng tr nh # ng th ng i qua hai i m A v B n m tr n � � � � � � � � � � � � ��
th c ho nh � � � �� l n l# t l -2 v 1 C u 4 ( 3 i m ) � � � � � � � Cho h nh vu ng � �ABCD , tr n c nh BC l y 1 i m M # ng tr n # ng k nh AM c t # ng tr n � � � � � � � � � � � � � � �
# ng k nh BC t i N v c t c nh AD t i E Ch ng minh E, N , C th ng h ng G i
F l giao i m c a BN v DC Ch ng minh # EMBED Equation.3 ###Ch ng minh r ng� � � � � � � �
MF vu ng g c v i AC � � � �� s 5 C u 1 ( 3 i m ) � � � � Cho h ph# ng tr nh : # EMBED � � �Equation.3 ###Gi i h ph# ng tr nh khi m = 1 Gi i v bi n lu n h ph# ng tr nh� � � � � � � � � � �theo tham s m T m m � � �� x y = 2 C u 2 ( 3 i m ) Gi i h ph# ng tr nh : # � � � � � � � �EMBED Equation.3 ###Cho ph# ng tr nh b c hai : ax2 + bx + c = 0 G i hai nghi m� � � � �
c a ph# ng tr nh l x1 , x2 L p ph# ng tr nh b c hai c hai nghi m l 2x1+ 3x2� � � � � � � � � � �
v 3x1 + 2x2 C u 3 ( 2 i m ) � � � � Cho tam gi c c n ABC ( AB = AC ) n i ti p � � � �
# ng tr n t m O M l m t i m chuy n ng tr n # ng tr n T B h # ng
Trang 170th ng vu ng g c v i AM c t CM D � � � � � � Ch ng minh tam gi c BMD c n C u 4 � � � �( 2 i m ) T nh : # EMBED Equation.3 ###Gi i b t ph# ng tr nh : ( x 1 ) ( 2x + � � � � � � � �
3 ) > 2x( x + 3 ) �� s 6C u 1 ( 2 i m )� � � � Gi i h ph# ng tr nh : # EMBED � � � �Equation.3 ###C u 2 ( 3 i m ) � � � Cho bi u th c : # EMBED Equation.3 ###R t � � �
g n bi u th c A Coi A l h m s c a bi n x v � � � � � � � � � �� thi h m s A C u 3 ( 2 i m )� � � � �
T m i u ki n c a tham s m � � � � � � �� hai ph# ng tr nh sau c nghi m chung � � � �
x2 + (3m + 2 )x 4 = 0 v x2 + (2m + 3 )x +2 =0 C u 4 ( 3 i m ) � � � � � Cho # ng tr n t m O v # ng th ng d c t (O) t i hai i m A,B T m t� � � � � � � � � � � � � �
i m M tr n d v hai ti p tuy n ME , MF ( E , F l ti p i m ) Ch ng minh g c
kh ng gi i ph# ng tr nh l p ph# ng tr nh b c hai m c hai nghi m l : # EMBED � � � � � � � � � � � �Equation.3 ### v # EMBED Equation.3 ### C u 3 ( 3 i m ) Cho x2 + y2 = 4 T m� � � � �
gi tr l n nh t , nh nh t c a x + y Gi i h ph# ng tr nh : # EMBED Equation.3� � � � � � � � � � �
### Gi i ph# ng tr nh : x4 10x3 2(m 11 )x2 + 2 ( 5m +6)x +2m = 0 C u 4 ( 3� � � � � � �
i m )
� � Cho tam gi c nh n ABC n i ti p # ng tr n t m O # ng ph n gi c � � � � � � � � � � � �trong c a g c A , B c t # ng tr n t m O t i D v E , g i giao i m hai # ng � � � � � � � � � � � � � �
ph n gi c l I , # ng th ng DE c t CA, CB l n l# t t i M , N Ch ng minh tam � � � � � � � � � � �
gi c AIE v tam gi c BID l tam gi c c n Ch ng minh t gi c AEMI l t gi c � � � � � � � � � � � �
n i ti p v MI // BC T gi c CMIN l h nh g ? � � � � � � � � �� s 8 C u1 ( 2 i m ) T m m � � � � � ��ph# ng tr nh ( x2 + x + m) ( x2 + mx + 1 ) = 0 c 4 nghi m ph n bi t C u 2 ( 3� � � � � � �
i m )
� � Cho h ph# ng tr nh : # EMBED Equation.3 ###Gi i h khi m = 3 T m m � � � � � � ph# ng tr nh c nghi m x > 1 , y > 0 C u 3 ( 1 i m )
d# ng tho m n x5+y5 = x3 + y3 Ch ng minh x2 + y2 # EMBED Equation.3 ### 1 + � � � �
xy C u 4 ( 3 i m ) Cho t gi c ABCD n i ti p # ng tr n (O) Ch ng minh AB.CD� � � � � � � � � � �+ BC.AD = AC.BD Cho tam gi c nh n ABC n i ti p trong # ng tr n (O) # ng k nh � � � � � � � � � �
AD # ng cao c a tam gi c k t � � � � � � ��nh A c t c nh BC t i K v c t # ng tr n (O)� � � � � � � �
t i E Ch ng minh : DE//BC Ch ng minh : AB.AC = AK.AD G i H l tr c t m c a � � � � � � � �tam gi c ABC Ch ng minh t gi c BHCD l h nh b nh h nh � � � � � � � � �� s 9 C u 1 ( 2 � �
i m )
� � Tr c c n th c m u c c bi u th c sau :� � � � � � � � # EMBED Equation.3 ###;
# EMBED Equation.3 ###; # EMBED Equation.3 ###C u 2 ( 3 i m ) � � � Choph# ng tr nh : x2 ( m+2)x + m2 1 = 0� � � � (1)G i x1, x2 l hai nghi m� � �
c a ph# ng tr nh T m m tho m n x1 x2 = 2 T m gi tr nguy n nh nh t c a m � � � � � � � � � � � � � � ph# ng tr nh c hai nghi m kh c nhau C u 3 ( 2 i m )
Equation.3 ### L p m t ph# ng tr nh b c hai c c c h s b ng s v c c c � � � � � � � � � � � � � �nghi m l x1 = # EMBED Equation.3 ###C u 4 ( 3 i m ) � � � � � Cho hai # ng tr n � � �(O1) v (O2) c t nhau t i A v B M t # ng th ng i qua A c t # ng tr n � � � � � � � � � � � � �(O1) , (O2) l n l# t t i C,D , g i I , J l trung i m c a AC v AD Ch ng minh � � � � � � � � � �
t gi c O1IJO2 l h nh thang vu ng G i M l giao di m c a CO1 v DO2 Ch ng � � � � � � � � � � �minh O1 , O2 , M , B n m tr n m t # ng tr n E l trung i m c a IJ , # ng � � � � � � � � � � � �
th ng CD quay quanh A T m t p h p i m E.X c � � � � � � � ��nh v tr c a d y CD � � � � �� d y CD �
c � �� d i l n nh t � � � �� s 10C u 1 ( 3 i m ) 1)V � � � � � �� th c a h m s : y = # � � � �EMBED Equation.3 ###2)Vi t ph# ng tr nh # ng th ng i qua i m (2; -2) v (1 ; � � � � � � � � � �-4 ) T m giao i m c a # ng th ng v a t m # c v i � � � � � � � � � � � � �� th tr n C u 2 ( 3 � � �
i m )
� � a) Gi i ph# ng tr nh : � � � # EMBED Equation.3 ###b)T nh gi tr � � �
c a bi u th c # EMBED Equation.3 ### v i # EMBED Equation.3 ###C u 3 ( 3 i m )� � � � � � �
Cho tam gi c ABC , g c B v g c C nh n C c # ng tr n # ng k nh AB , AC� � � � � � � � � � � �
c t nhau t i D M t # ng th ng qua A c t # ng tr n # ng k nh AB , AC l n � � � � � � � � � � � � � �l# t t i E v F Ch ng minh B , C , D th ng h ng Ch ng minh B, C , E , F n m � � � � � � � �
th tr n C u 2 ( 3 i m ) Gi i ph# ng tr nh :# EMBED Equation.3 ###Gi i ph# ng � � � � � � � � � �
tr nh : # EMBED Equation.3 ###C u 3 ( 3 i m ) � � � � Cho h nh b nh h nh ABCD , # ng � � � � �
ph n gi c c a g c BAD c t DC v BC theo th t t i M v N G i O l t m # ng � � � � � � � � � � � � � � �
tr n ngo i ti p tam gi c MNC� � � �