MC vdi (O) (C la tiep diem) Ke CH vuong goc vdi AB (He AB), MB cat
c) TimX d eA <
• X2 = - 2 t h i X | = = 2- X 2 = 2 + 2 = 4 Ta CO : -2m^ = X|X2 = 4.(-2) <=>m^ = 4<=>m = ± 2 Vay m = 2 hoac m = - 2 .
Nhan xet : V i tdng ciia hai nghicm la hhng so (X| + X2 = 2), do vay icct hOp vi'd
he thiJc nghiem cho IriTdc (xf = 4x2 ) g'^P ' ™ ^^^'^ ^ i ' ^2- TiTdo tim diTOc m.
Bai 4: NiSfa chu vi hinh chỉ nhat la : 28 : 2 = 14 (m)
14 i Goi chieu rong cua hinh chiJ nhal la x (m) (Dieu kien 0 < x < ^ ~ ^) ' " Goi chieu rong cua hinh chiJ nhal la x (m) (Dieu kien 0 < x < ^ ~ ^) ' " Chieu dai cua hinh chu" nhat la 14 - x (m)
Theodjnh l i Py-ta-go ta co : x^ + (14 - x)^ = 10^ o x^ + 1 9 6 - 28x + x^= 100 o 2x^ - 28x + 96 = 0 x^ - 14x + 48 = 0
Á = 4 9 - 4 8 = 1 ; VA' = 1 - > X | = 8 > 7 (loai) ; X2 = ^ ^ = 6 (nhan) Vay chieu rong cua hinh chiJ nhat la 6m.
Chieu dai cua hinh chCT nhat la : 14 - 6 = 8 (m)
Nhan xet : Ghi nhd rhng AABC vuong tai A => AB^ + A C ' = BC^
Bai 5: a)Ta co: AB AC (AB = AC), AD lii diTclng kinh cua di/cing tron (O) (gt) => BD = CD =^ B M D = CMD.
Vay M D la dÚctng phan giac cua goc BMC.
b) Ta CO : A B D = A C D = 90" (goc npi tiep chan nijfa du^dng tron) ADB = ACB (hai goc noi tiep ciing chán cung AB) ADB = ACB (hai goc noi tiep ciing chán cung AB)
Ma ACB = 60" (AABC dcu) nen ADB = 6O".
AABD vuong tai B => AB = ADsin ADB , BD = ADcos ADB AB = 2Rsin60" = >/3 R, BD = 2R.cos60" = R
Do vay SABD = - A B . B D = -.V3 R.R =
Túdng tie CO SACD = •
Vay SAIHX: = SABD + SACD = V3 R^ (dvdt)
Cty TNHH MTV DWH Khang Vigt
Yi BD = CD => K A H = K M H => TiJ giac K M A H noi tiep
KHD = iCMA ' " • Ivla K M A = 90" (goc noi tiep ch^n nijTa difdng tron (O)). Do d6 K H D = 90".
X6t AKAD CO A M , BD, HK la ba diTdng cao
(vi A M 1 D K ( K M A = 90"), BD 1 A K ( A B D = 90"), K H 1 A D ( K H D = 90")). V$y ba dtfdng thang A M , BD, HK dong quỵ
Nh§n xet:
a) Cac goc noi tiep ciing ch^n mot cung hoac cac cung bang nhau thi bKng nhaụ b) Chu y rang ADB = 60" va trong tarn giac vuong, moi canh goc vuong b^ng: b) Chu y rang ADB = 60" va trong tarn giac vuong, moi canh goc vuong b^ng:
Canh huyen nhan vdi sin goc doi hoac nhan vdi cosin goc kẹ
c) Nhan ra rang A M , BD, HK la ba diTdng cao cua tam giac KAD. . 1 - sr^
SO 27
D E THI T U Y E N SINH VAO L(3P 10 THPT, T P . H A NOỊ NAM HQC 2011 - 2012 NAM HQC 2011 - 2012
Bai 1: (2,5 diem) Cho A = - -!^^^^^^ ^ — vdi x > 0 va x ^ 25.
Vx - 5 X - 25 Vx + 5 a) Rut gon bieu thiJc Ạ
b) Tim gia tri cua A khi x = 9. t
c) Tim X de A < - . 3 3
Bai 2: (2,5 diem) Gidi hai loan sau banf^ each lap phucm^ trinh hoac he phucfng trinh:
Mot doi xe Iheo ke" hoach chd hét 140 tan hang trong mot so ngay quy dinh. Do moi ngay doi do chd vúdt miJc 5 tan nen doi da hoan thanh ke hoach
S(Jm hcJn thdi gian quy dinh 1 ngay va chct them di/dc 10 tan. Hoi iheo ké hoach dpi xe chd hang hét bao nhieu ngay ?
J^ai 3: (1 diem) Cho parabol (P): y = x^ va diTdng thing (d): y = 2x - m^ + 9. ^) Tim toa dp cac giao diem cua parabol (P) va di/dng thing (d) khi m = 1. ^) Tim m de dirdng thing (d) c i t parabol (P) tai hai diem n^m ve hai phia ciia
iruc tung.
4: (3,5 diem) Cho diTdng tron tarn O, diTdng kinh AB = 2R. Goi d, va Ian IWt la hai tiep tuyen cua diTdng tron (O) tai hai diem A va B. Gpi I la trung IWt la hai tiep tuyen cua diTdng tron (O) tai hai diem A va B. Gpi I la trung ^Jem cua OA va E la diem thupc diTdng tron (O) (E khong trung vdi A va B). Dirdng thing d di qua diem E v^ vuong goc vdi EI c i t hai diTdng thing d,, d2
Ian lirpt tai M , N .
Luy^n giai d6 triiOc kl thi vao \dp 10 ba mign BJc, Trung, Nam mOn Toan _ NguySn Dijfc Ta'n
a) ChiJng minh A M E I la tu" giic noi tiep.
b) Chu-ngminh E N I = E B I va M I N = 90". r. H i i >i