D B1 OB^ CH ± OBC HO =90 "
b) Goi Ax la tiep tuyen cua du-dng tr6n (O) Ta c6 OA 1 Ax.
Ma xAF - ACB (He qua goc tao bcTi tia tiep tuyén va day cung)
ACB = AFE (BCEF npi tiep)
Do do xAF = AFE , xAF va AFE so le trong nen Ax // EF
Ta CO Ax // EF, OA 1 Ax ,
Vay EF 1 OẠ ' • * '"''^ > + '^v •<••'
c) Goi K la giao diem cua A D va dufdng tron (O) (K A ) ^[ ^,£"3 ;1?w c
Ve 0 1 1 BC tai I , goi O la diem doi xuTng qua O qua I . ^ '^^' Ta CO I la trung diem cua BC. Do vay BOCÓ la hinh binh hanh = > 0 ' B = OC = R, 0 ' C = OB = R
Ta CO HBD = DAC (ciing phu vdi A C B ) ,
DBK = DAC (hai goc ngi tiep cijng ch^n cung CK) Do do HBD = DBK
ABHK c o j B D vufa la difdng cao (BD 1 M) viTa m difcJng phan giac BC la dirdng trung tri/c cua HK.
( H B D = D B K ) ^ A B H K can tai B
Nen H , K dói xuTng qua B C .
Ma O ' , O doi xu-ng qua B C . Do do O ' H = O K = R (Tinh chat doi xỉng true) Ta c6 0 ' B = 0 ' H = 0 ' C = R
Vay ban kinh di/dng tron ngoai tiep tarn giac B H C bang R ' Nhan xet: Day la bai toan hinh hoc cd ban.
Bai 4. Gia suT cd hinh chff nhat A B C D
( A B = 4, B C = 3) E , F , G , H Ian lifdt tren cae canh A B , B C , C D , D A ( E F = x,
F G = y, G H = z, H E = t)
Ap dung dinh l i Py-ta-go vao c^c tarn giac vudng B E F ( B = 90"), C F G ( C = 90"), D G H ( D = 90"), A H E ( A = 90"). Ta cd E F ^ = BÊ + B F ^ , F G ^ = C F ^ + C G ^ , G H ^ = D G ^ + D H ^ H E ^ = A H ^ + A E ^ Ma A E ' + B E ' < A E ' + B E ' + 2AẸBE = ( A E + B E ) ' = 16 Ti/dng tir B F ^ + C F ^ < 9, C G ' + D G ' < 16, D H ' + A H ' < 9 Do đ E F ^ + F G ^ + G H ^ + H E ^ < 16 + 9 + 16 + 9
Luygn giai dg trade ki thi vAo I6p 10 ba miSn Bjc. Trung, Nam mfln Toan _ Nguygn Ottc Jjn
Vay + + + < 50
2 . , r^ 2 (AE + BE)2 + (AE + BE)^ ^ (AE + BE)2 -
Mat khac AÊ + BÊ = ' — ^ > ^ —
S 2 2 . \ , / • y AB^ 4^ „ • O-' 'V>'' TMng tir BF^ + CF^ > 4,5 ; CG^ + DG^ > 8 ; D H' + AH^ > 4,5 4. ; ( ; Do do EF^ + FG^ = G r f + HÊ > 8 + 4,5 + 8 + 4,5 * A iv Vayx^ + ý + z' + t^>25 '••''^ xA'l nv Tom lai, ta c6: 25 < + y^ + + t^ < 50
Nhan xet: Day la bai todn ve bat d^ng thiJc hinh hoc. Thifc chat la bai todn: v d i a , b > 0 r w i n CM
Chufng minh r^ng: ^ ^ - ^ ^ < â + b^ < (a + b)^ va ket hdp vdi dinh ly Py-ta-gọ
; • D^sosi
DE THI TUYEN SINH VAO LdP 10 CHUYEN TOAN THPT. CHUYEN PHAN BQI CHAU TINH NGHE AN, NAM HQC 2012 - 2013 Cau 1. (3,5 diem)