a,
ta co : dc la tiep tuyen cua (O) tai C
=> OC vuong goc CD
=> goc OCD bang 90 do
xet tu giac OHDC co
goc OHD + goc OCD = 90 do + 90 do = 180 do
=> tu giac OHDC nt
b,
ta co : OC=OB(=ban kinh)
CD=BD ( tinh chat tiep tuyen cat nhau)
Do đó : OD la trung truc cua BC
=> OD ┴ BC
=> goc OIK = 90 do
xet ∆OIA va ∆ OHD co
goc AOI chung
goc OIA = OHD (=90 do)
=> ∆ OIA dong dang ∆OHD
=> OI/OH = OA/OD
=> OI x OD= OAxOH

c )
Xet ∆ OCD co goc OCD =90 do ,CI ┴ OD
=> OC^2 = OIxOD
mặt khác : OC=OM(=ban kinh)OHxOA=OIxOD(cm phan b)
Do đó OM^2 = OHxOA
=> tg OMA vuong tai M
=> OM┴MA
=> AM la tiep tuyen cua (O) tai M
d )
goi K la giao diem cua OA vs (O)
S ,S1, S2 lan luot la dien tich phần∆ OAM nằm ngoài đường tròn(O) , cung KM
va∆OMA
∆ OMA vuong tai M
co OM=R,OA=2R=> OA=2OM
=> goc MAO = 30 do
=> goc AOM = 60 do
=> sđ cung MK = 60 do
=> S1 = ( π x R^2 x 60)/360 = π x R^2 /6
ap dung dinh li pita go vao ∆ OMA co
OA^2=OM^2 = MA^2
=> MA = √(OA^2-OM^2)
=> MA = √3 x R
=>S2= 1/2 OM x MA=1/2 x R x can 3 R=√ 3 x R^2 /2
vay S = S2 - S1
= (√3 xR^2 x π R^2 )/12