. T\ giac IA CJ la hinh binh hanh OJ= AI ==
1)Giai phiTPng trinh: (x \= l-x^ X1
AID = AOH AAID ^ AAOH (g.g)
8 . V , '
1 Al_ ^ AD ^ AD.AO = AỊAH. Ma A l = ^ A H , AO = - B C . Al_ ^ AD ^ AD.AO = AỊAH. Ma A l = ^ A H , AO = - B C . AO A H ^ 2 2 . AABC vuong tai A, AH la diTcJng cao => AH^ = HB.HC.
1 BC 1 HC + HB
Do do HB.HC = AD.BC AD HB.HC AD HB.HC
1 1 I
— + —
AD HB HC
3) Ta CO PKM = ANM (TuT giac ANMK noi tiep),
A N M = MBC (Tu" giac MNCB noi tiep) => MBC = PKM . TiJ giac PKMB npi tiep ^ PKB = PMB . Ma PMB = BCN .
Nen PKB = BCN TuT giac BKAC npi tiep. Do do BKC = BAC - 90". 4) AABC vuong tai A, AH la dirdng cao
, =:^_l-=-L + -L va B d ^ A B ^ + A d ^ - ^ = i + 7 r i ,
AH^ AB^ A d AH^ 8^
BC' = 6' + 8^ Nen AH = 4,8 va BC = 10.
Gpi J la tam diTdng tron (BMN) => J la tam dtrdng tr6n (BMNC)
IJ 1 M N , J I 1 BC. Do do AI // JI, JI // OA
. T\ giac I AC J la hinh binh hanh OJ = A I = = 2.4
A O B J vuong tai O => J B ' = O B ' + CJ' = 5' + 2,4' = 769 25 JB = V769 ' > - / . V769
Vay ban kinh cua diTdng tron ngoai tiep tam giac BMN la
Nh$n xet: Day la bai todn hinh hoc quen thuoc, ve them tam J cua difcJng
N/769 tron (BMNC) de xuát hipn hmh binh hanh lAOJ, tiT do den JB = ^ tron (BMNC) de xuát hipn hmh binh hanh lAOJ, tiT do den JB = ^ hoan tôn tir nhien.
la
Cty TNHH MTV DWH Khang Vi$t
D E S O 38
DE THI TUYEN SINH VAO LfiP 1 0 CHUYEN TOAN
TRl/dNG OAI HQC SI/ PHAM, TP.H5 CHÍ MINH NAM HOC 2012 - 2013
Caul.(2dilm) _ _ n r L i r J ' , .1
1) Giai phiTPng trinh: (x - \ = l-x^. X 1 X X
3 1 . 2
2) Cho a, b la cac so thiTc thoa man: â - 3â + 8a = 9 va b^ - 6b' + 17b = 15. Tinh a + b. ; : , , ,.
CSu IỊ (2 diem) (adsbygoogle = window.adsbygoogle || []).push({});
1) Cho m, n la hai só nguyen. ChiiTng minh rang neu 5(m + n)' + mn chia hét cho 441 thi mn cung chia hot cho 441. cho 441 thi mn cung chia hot cho 441.
1) Cho m, n la hai só nguyen. ChiiTng minh rang neu 5(m + n)' + mn chia hét cho 441 thi mn cung chia hot cho 441. cho 441 thi mn cung chia hot cho 441. ( l + x ' ) ( l + y ' ) > ( x + y ) ( l + x y )
2) Cho a, b la hai só thiTc dúdng. Tim gi^ trj nho nhát cua bieu thuTc ab a + b ab a + b
Cau IV. (3 diem)
1) Cho tam giac ABC c6 B, C co dinh va A di dpng sao cho AB = 2AC.
a) Gpi I la diem tren canh BC sao cho IB = 2IC. Chtfng minh A I la tia phan giac cua goc BAC. giac cua goc BAC.
b) Chiang minh r^ng A luon di dpng tren mot diTdng tron co dinh.
2) Cho tam gidc ABC. Du'dng Iron npi tiep tam giac ABC co tam I , tiep xiic voti BC tai D. Du'dng tron bang tiep goc A cua tam gidc ABC co tam J, tiep xuc BC tai D. Du'dng tron bang tiep goc A cua tam gidc ABC co tam J, tiep xuc vdi BC tai Ẹ
a) Gpi F la giao diem cua AE va DỊ ChiJfng minh ring F thuoc difdng tron (I). b) Gpi M la trung diem cua BC. ChiJug minh ring du'dng thang M I luon di b) Gpi M la trung diem cua BC. ChiJug minh ring du'dng thang M I luon di
qua trung diem cua AD.
CSu V. (1 diem). Tir 625 so ti/ nhien I , 2, 3 624, 625 ta chpn ra 312 so sao cho khong co hai so nao co tdng b^ng 625. Chufng minh ring trong 312 sd du'pc chpn, bao gid cung co it nhat mot sdchinh phu'Png.
HI/6NG DAN GIAI Cau Ị Cau Ị
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