M, D, E ,N thang hang ^ J,
c) Gpi giao diem cua BE va CF vdi diTdng tron (O; R) Ian liTdt laM, N.
Ta co: B C F = B E F (hai goc npi tiep ciing chan B F cua diTdng tr6n (BFEC)) BCF = B M N ( h a i goc npi tiep ciing chan B N cua drfdng tron (O; R)) => I K // M N (cap goc dong vi bhng nhau) K N = M I (2 cung chin giCra 2 day //) |, M a E B F = E C F (2 goc npi tiep cung ch^n E F ) => A M = A N
LuyQn giii a6 truflc k1 thi vio lOp 10 ba mign B^c, Trung N j , niO:: i',an _ NguyJn Pdc TS'n
=ịsdSl + s d f ^ = s d A M + sdMI=>AI = AK=> AI = AK (1)
Lai c6: SK = SI (tinh chaft hai tiep tuyen c^t nhau cua mot du^ng Irbn) (2) OK = OI (ban kinh) (3)
Tir (1), (2), (3) => O, A, S thing hang (cilng n^m tren dif&ng trung trifc ciia IK) d) Ke OP 1 BC. Dung ti so liTOng giac tinh diTdc BC = R 73
AE EF '
, ChiJng minh diTOc: AAEF ^AABC => — = — " oiikJ r- /
AB BC
Mk A A E B \k nufa tam giac dcu (BAC = 60'\ = 90") = i = > E F = - B C = - R V 3 AE 1 AB 2 c) EF ^ BC 2 2 " ~ 2 => Sp.Ho = ^ OẠEF = i R. = (dvdt) D]6s674
Bai 1: (2 diem) Giai cdc phi/dng trinh va he phifdng trinh sau:
a) 3x' - 26x + 48 = 0 b) (x' - 1)' + (x' - 1) - 2 = 0 2x - 3y - 2V7
3x - 4y = 3V7 - 1
Bai 2 :(1,5 diem) Thu gon cac bieu thifc sau:
A= : ^ . V ^ T ^ '
V>/5-l
aV^ + bVb _aVb-fbV^ (vdia>0.b>0) a + b - vab vab
Bai 3: (1,5 diem) Cho parabol (P): y = y ^irdng thing (d): y = - - + 1.
a) Ve (P) va (d) tren ciing mot he true toa dp.
b) Tim phiTdng trinh di/5ng thing (d') song song vdi (d) va tiep xuc (P).
Bai 4: (1,5 diem) Cho phifdng trinh; x^ - 2(m - l)x - 4m = 0 vdi m la tham sí
va X la an sọ
a) ChiJng to phiTdng trinh luon c6 nghiem vdi mpi gid tri ciia m. b) Tim m de phiTdng trinh c6 hai nghiem X|, X2 thoa h0 thuTc:
xf + X j - Xi - X2 = 6
Cty TNHH M1V i j W i ; Kliany Vi^i
ai 5: (3,5 diem) Cho tam giac nhon ABC noi tiep trong dtfdng tron (O; R)
(AB > AC). Gpi H la giao diem cua hai diTdng cao BD va CE cua tam gidc ABC, F la giao diem cua AH va BC. .
a) ChiJng minh tuf giac BEHF npi tiep. j ;
b) ChiJng minh: FẠFH = FB.FC '*
c) Ve dirdng kinh AI cua di/cJng tr6n (O). Gpi K la diem doi xuTng vdi H qua BC. Chiang minh tỉ giac BIKC la hinh thang can.
va ACB - ABC= 30". Tinh dien tich cua tiJ giac ABIC d) Cho BC =
theo R.
HlT^NG D A N G I A I
Bai 1: a) 3x^ - 26x + 48 = 0, A" = b'^ - ac = (-13)^ - 3.48 = 25 > 0
PhiTdng trinh c6 2 nghiem phan biet: x, = ~ ^ ' ^ ^ = 6 ; X2 = ~^ ~ ^ = -
a a 3 b) (x^- l)^ + (x^- l ) - 2 = 0 (1)
Datt = x ' - 1 (t>-l). K h i d 6 ( l ) o t S t - 2 = 0 (2)
a + b + c = 0=> PhiTdng trinh (2) c6 2 nghiem: t, = 1 (nhan); tj = - = - 2 (loai) a
t = 1 <=>x^ - 1 = 1 <=>x^ = 2 o x = + ^
Co the diTa ve phu-dng trinh trung phiTdng: x'' - x^ - 2 = 0. Ta c6: x = ± N/2
'2x - 3y = 2V7 |-6x + 9y = -67? jy = -2 3x - 4y = 3V7 - 1 [6x - By = 6V7 - 2 l2x - 3y = 27? y = -2 c) # = V 7 - 3 ' Bai 2: A = . ^ ^ . ^ 7 ^ f(3-V5)(2.275) (6 - 2V5)(l + yfs) t ^ ^ f i i ± ^ = V(rarwf)=74=2
B = a + b - Vab yfab aVa + hyjh ayfb + h^f^L
^ 5 - 1
j v^ + V b ) ( a - f b- v ; i ^ ) _ v^ ( . ^ + V b ) ^ ( ^ ^ ^ ) _ ( ^ ^ ^ ) ^ o
Luỷn g\i\^ KI th, . u i Idp 10 ba mijn B^c. Trung, Nam mOn ToAn _ IMguySn Dijfc Ta"n
Bai 3:
a) • Bang gia tri:
X -2 - 1 0 1 2 2 2 1 2 0 1 2 2 X 0 2 1 0
Do thi ham so:
b) (d'): y = ax + b song song (d):
X , 1
y = — + l = > a = —
^ 2 2 Phi/dng Irinh hoanh do giao diem Phi/dng Irinh hoanh do giao diem cua (?) va (d'): ^ = - ^ + b c ^ x ^ + x - 2b = 0. A = b ^ - 4 a c = l ' - 4 . 1 . ( - 2 b ) = 1 + 8b 2 2 y / /(P) 2 / i V 2 -2 - 1 O 1 X
(d') tiep xuc (P) => PhiTcJng trinh c6 nghiem kcp => A = 0 => b =
V a y ( d ' ) : y = - | - ^ f
Bai 4: a) A ' = b'^ - ac = [ - ( m - l ) f - l . ( - 4 m ) = mU 2m + 1 = (m + 1)^>0, V PhiTcfng trinh luon c6 nghicm, Vm.
I l l