D thing hang.
1) X6t AHAF va AHKB c6 AH F= KHB (doi dinh), HAF HKB (Hai g6c noi tiep cilng ch^n cung BF)
Cty TNHH MTV DWH Khana Vi§!
Do do A H A F A H K B (gt) HA HF • HẠHB = HF.HK
A} tie, ''
HK HB M A , MB la cac tiep tuyén cua diTdng tron (O) M A , MB la cac tiep tuyén cua diTdng tron (O)
=> M A 1 OA, M O la tia phan giac goc A M B va M A = M B .
AAMO vuong tai A, A H la diTdng cao => A t f = HM.HỌ Ma A H = HB. Do vay HM.HO = HF,HK (= HẠHB)
X ^ t AHMK va AHFO c6 M H K = FHO (dói dinh)
2)
Do do AHMK ^ AHFO (c-g-c) ^ H M K = HFO => TO gidc KMFO npi tiep. Ma OK = OF (= R) =^ OK = OF => O M K = OMF
Vay MO la tia phan giac cua g6c KMF. X e t A I A K va A I B A c o :
A I K (Chung), l A K = IBA (He qua goc tao bdi tia tiep tuyen va day cung) lA IK
Do do AIAK ^ AIBA (g.g) =^ — = — . Ma l A = I M ( I l a trung di^m cua IB l A
M A ) . Nen I M _ JK IB ~ I M
Xet AIMK va A I B M cd M I K (chung), I M I K IB I M
Do d6 AIMK ^ AIBM (c-g-c) => I M K = I B M . Ma I B M = KCB (He qua goc tao bcli tia tiep tuyen va day cung)
Do do I M K = iCB (= IBM) z:> MA // BC. Do vay AB = AC
Suy ra AB = AC. Vay tam gidc ABC can tai Ạ — ' Nhan xet: Day la bai loan hinh cd ban, quen thuoc doi vdi mpi hoc sinh Idp 9.
Luy^n g\i\ U[i6c ki thi vao Idp 10 ba mjgn Bjc. Trung, Nam iiifvi loan _ NguySn Difc Tin
i>l§ S O 48
DE THI TUYEN SINH VAO LdP 10 THPT CHUYgN TOAN,
TiNH QUANG NGAI, NAM HOC 2012 - 2013 Bai 1. (2,0 diem) | /
5V3+ 3V5
2) Cho hai so" x, y thoa man + y^ - 2xy - 2x + 4y - 7 = 0. Tim gii tri cua x
khi y dat gia tri Ictn nhal
Bai2.(2,0digm) HAHA 6I> o,:,
1) Giai phiTdng trinh: x^ + 2 = 3v3x^-2 • : ' ^ 1^ 1 , ^
2) Giai he phiTdng trinh: y X xy
X + xy + y = 5 ,
Bai 3, (2,0 diem)