MC vdi (O) (C la tiep diem) Ke CH vuong goc vdi AB (He AB), MB cat
a) Cantim each ch^ng min hÁ > 0, vdi moi m.
b) Theo he IhuTc V i- c t , ta cd x, + X2 = 2m ; X|X2 = - 4 m - 5. D o vay A = x^+ X j - X| X 2 = 4m^ + 12m + 15 D o vay A = x^+ X j - X| X 2 = 4m^ + 12m + 15
Tit do de tim diTdc gia tri nho nhat cua A .
B a i 5: a) B A C = 90" (gdc noi tiep ch^n nuTa diTdng tron)
H E A = 90" ( H E 1 A B ) , H F A = 90" (HF 1 A C ) => TO giac A E H F la hinh chiJr nhat. Gpi J la giao d i e m cua A H va EF. TO giac A E H F noi tiep diTdng tron tam J
JA = JF => A J A F can tai J => JFA = JAF
~X7T7 imnn iin i v u v v i i rvriaiiy vỉi
M a O A = OC ( = R ) => A O A C can tai O => O A C = O C A N e n C A C + JFA = O C A + JAF b) = 180" - A H C = 180" - 90" = 90" V a y O A 1 EF O A -L EF (chufng m i n h tren) => PA = Q A => A B P = A P E X e t A A B P va A A P E co B A P (chung), A B P = A P E D o do A A B P ^ A A P E (g.g) A P A B A P ' = A E . A B c) A d) A E A P
A H A B vuong tai H , H E la di/dng cao => A t f = A E . A B
Ta cd : A P ' = A H ' ( = A E . A B) ^ A P = A H => A A P H can tai A .
A O A D cd A H , D E la hai diTdng cao ( D E 1 O A , A H 1 O D ) c^t nhau tai J J la triTc tam cua tam giac O A D => OJ 1 A K => OJ di qua trung diem cua A K . N e n OJ la dúdng trung triTc cua doan thang A K =:> JK = JA
=> K thupc dirdng tron (J).
Ta cd A , K , F, H , E cung thupc mot dtfdng tron (J). Do vay tií giac A E F K noi tiep.
Ta cd : D C K = B A K ( t t f g i a c A K C B npi tiep) D F K = E A K (tỉ giac A E F K npi tiep)
D C K + I C K = D F K + I F D = I 8 O " (ke b i i ) 3 ^ I C K = I F D X e t A I C K va A I F D cd C I K (chung), I C K = I F D I C I K D o d d A I C K ^ A I F D (g.g) I F I D I F . I K = I C . I D
M a t khac I H F = H A F (cung phu v d i A H F ) ,
H K F = H A F ( A , K , F, H , E cung thupc mot diTdng tron) I H F = H K F X e t A I H F va A I K H cd H I F (chung), I H F = H K F I H I F I F . I K = I H ' a) Do do A I H F ^ A I K H (g.g) V a y I H ' = I C . I D ( = I F . I K ) Nhan x e t : Tỉ giac A E H F cd B A C = 90", H E A = 90", H F A = 90". Chu y rkng: O A C = O C A , JFA = J A F (J la giao d i e m cua A H va EF)
Luy$n giai dg truOc k1 thi vao Idp 10 ba mign 6^0. Trung, NarrTmOn Toan _ Nguy6n Ddc W\ OA ± EF (la bai loan quen thuoc d Idp 8)
b) AP' = A H ' (= AẸAB) => AP = AH.
Dc chiirng minh hai doan thang AP, AH bang nhau nhieu khi phai nghi den chi^ng minh AP' = A H ' néu Irong hinh ve bai loan c6 xuát hi^n lam giac
vuong, cac lam giac dong dang... a :| . ,i ,'
c) De Iháy A, E, H, F cilng thuoc diTdng Iron (J ; JA). jj ''Rff/iar-'jil ,,.) . Tim each chrfng minh JK = JẠ Tim each chrfng minh JK = JẠ