a)hình bạn tự vẽ nha chứ mik vẽ lâu lắm
b)ta có:
\(\Delta\)OAB đồng dạng với \(\Delta\)OA'B':
\(\Rightarrow\dfrac{OA}{OA'}=\dfrac{AB}{A'B'}\)
\(\Delta\)OIF' đồng dạng với \(\Delta\)A'B'F'
\(\Rightarrow\dfrac{OI}{A'B'}=\dfrac{OF'}{A'F'}\)
\(\Leftrightarrow\dfrac{AB}{A'B'}=\dfrac{OF'}{OA'-OF'}\)
\(\Leftrightarrow\dfrac{OA}{OA'}=\dfrac{OF'}{OA'-OF'}\)
\(\Leftrightarrow OA.OA'-OA.OF'=OF'.OA'\)
chia hai về cho OA.OA'.OF'
\(\Rightarrow\dfrac{1}{OF}-\dfrac{1}{OA'}=\dfrac{1}{OA}\)
mà OA=2OF'\(\Rightarrow OF'=0,5OA\)
\(\Rightarrow\dfrac{1}{0,5OA}-\dfrac{1}{OA'}=\dfrac{1}{OA}\)
\(\Leftrightarrow\dfrac{1}{0,5OA}-\dfrac{1}{OA}=\dfrac{1}{OA'}\)
\(\Leftrightarrow\dfrac{2}{OA}-\dfrac{1}{OA}=\dfrac{1}{OA'}\)
\(\Leftrightarrow\dfrac{1}{OA}=\dfrac{1}{OA'}\Rightarrow OA=OA'\)
c)ta có:
\(\dfrac{OA}{OA'}=\dfrac{AB}{A'B'}\)
\(\Leftrightarrow\dfrac{h}{h'}=\dfrac{OA}{OA'}\)
mà OA=OA' nên:
\(\dfrac{h}{h'}=1\Rightarrow h=h'\)
d)ta có:
\(\dfrac{1}{OF'}=\dfrac{1}{OA'}+\dfrac{1}{OA}\)
mà OA=OA' nên:
\(\dfrac{1}{f}=\dfrac{2}{OA}\)
\(\Rightarrow f=\dfrac{OA}{2}=\dfrac{OA'}{2}\)