Q3 of 15 Page 92

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


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