a, \(\Delta AOB\infty\Delta A'OB'\Rightarrow\dfrac{OA}{OA'}=\dfrac{AB}{A'B'}\)
\(\Delta A'B'F'\infty\Delta OIF'\Rightarrow\dfrac{OI}{A'B'}=\dfrac{OF'}{A'F'}\)
\(\Rightarrow\dfrac{OF'}{OA'+OF'}=\dfrac{AB}{A'B'}\)
\(\Rightarrow\dfrac{20}{OA'+20}=\dfrac{1}{2}\Rightarrow OA'=20\)
Ta co: \(\dfrac{OA}{OA'}=\dfrac{1}{2}\Rightarrow OA=\dfrac{OA'}{2}=10\)
b, C/m tương tự câu a nhưng:
\(\dfrac{OF'}{A'F'}=\dfrac{AB}{A'B'}\Leftrightarrow\dfrac{OF'}{OA'-OF'}=\dfrac{1}{2}\)
=> OA' = 60 => OA = 30