Question

If O is the centre of the circle and chord AB = OA and the area of triangle AOB = 4√3 cm², then the area of the circle will be

(a) 4π cm² 

(b) 16π cm² 

(c) 24√3 cm² 

(d) 24π √3 cm²

Answer 1

(b) 16π cm².

AB = OA ⇒ AB = OA = OB (radii of circle are equal) 

⇒ ΔAOB is equilateral. 

∴ If ‘r’ is the radius of the circle,

then area of ΔAOB = \(\frac{\sqrt3}{4}\)side²

⇒ \(\frac{\sqrt3}{4}\)(r)² = 4√3 (given)

⇒ r² = 16 ⇒ r = 4

∴ Area of circle = πr² = 16π cm².