Find the relation between a side and the circumradius of an equilateral triangle.

AB = BC = CA

∠ABC = ∠ACB = ∠BAC = 60°

Let, AH = x cm

∴ AH = CH = BH = x cm

∴ DH = x/2 cm [∵H is circumcentre, ABC is equilateral]

In ΔAHD,

∠ADH = 90°

AH = x cm

HD = x/2 cm

∴ AB = 2 × AD = 2 × x√3/2 = x√3 cm

∴ side = √3 × circumradius