(a) 12√3 cm2
Since area of circle = 4π ⇒ πr2 = 4π ⇒ r = 2 cm
In ΔOAD,
tan 30° = \(\frac{OD}{AD}\) ⇒ \(\frac{1}{\sqrt3}\) = \(\frac{2}{AD}\)
⇒ AD = 2√3 cm
∴ AB = 2AD = 4√3 cm
∴ Area of equilateral ΔABC = \(\frac{\sqrt3}{4}\) (AB)2
= \(\frac{\sqrt3}{4}\) (4√3)2 = 12√3 cm2.