Let $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1,a>b$ be an ellipse with foci $F_1$ and $F_2$ Let $AO$ be its semi-minor axis, where $O$ is the centre of the ellipse. The lines $A{F}_1$ and $A{F}_2$, when extended, cut the ellipse again at points $B$ and $C$ respectively. Suppose that the $\mathrm{\Delta }ABC$ is equilateral. Then, the eccentricity of the ellipse is

• A

  $\frac{1}{\sqrt{2}}$
• B

  $\frac{1}{\sqrt{3}}$
• C

  $\frac{1}{3}$
• Correct answer
  D

  $\frac{1}{2}$

Hence, the correct answer is option: 'D'.