VE trung tuy6n BE cua tam giirc ABM.. a Chimg minh trEE =frr.. Cho nria dulng tron tdm O duong kinh AB, ban kfnh OC vu6ng g6c vdi AB.. Goi d la titip tuy6n v6i nria duong tíon tai Ạ Qua
Trang 1Tns t,d r-er
PHoNG GrAo DUC vA DAo rAo ttpx cuAu
on rnr voNG I, cHeN Hec sINH GIoI nuvpN LoP 9
NArvr Hec zot3-zor4 Mdn To6n - (Thdi gian ldm bdi 150 philt)
C6u Ị (4,0 tliOm)
1.Tinh:
a)
,|
"' z^,lt +il;' vl-z +2Jj' qJi +3Já "" zotzJzon+zlrzJ2lr3'
Cdu IỊ (3,5 di6m)
.
l Chimg minh r6ng:
a)Niiu a> b>o thi #=;[#-#),
4049 45
CAU IIỊ (5,5 di6m)
1 Giei c5c phucmg trinh sau:
a) J*+ự.6-t6=to; q Jf 4-2J-rs2=0.
2 Chimgminh ring vdi moi x, y ta c6 Uat Aang thric: *o * yo > xyt + x'y .
Cffu IV (5,0 di6m)
l Cho hinh binh hdnh ABCD c6 AC :2A8, M le giao tli6m cua hai ducrng
chdo AC vd BD VE trung tuy6n BE cua tam giirc ABM.
a) Chimg minh trEE =frr.
b) TU E h4 dudng vudng g6c v6i BM clt BC tai Ị Chrmg minh IB : IC.
2 Cho nria dulng tron tdm O duong kinh AB, ban kfnh OC vu6ng g6c vdi
AB Goi d la titip tuy6n v6i nria duong tíon tai Ạ Qua di6m M bat k! thuQc cung
AC (tru A vd C), ke titip tuytfn v6i dudng trdn, cit dt4i E vh czit dulng thing OC tai D Goi F ld giao tli6m cria BD va d Chtrng minh rdng tich AẸ kh6ng php thudc vdo vi tri ctadiOm M tr6n cung AC (tru A vd C)
Chung minh ring n6u a, b d€u ld t6ng cua 2 sd chinh phu8ng thi ab cfrng ld
t6ng cira 2 sd chinh phuong