Question 6

The radius of the circle circumscribing the three vertices of an equilateral triangle is 12 cm. Determine the height (in cm) of the equilateral triangle.

Solution

Let the median = height of the triangle = $$h$$ cm

ABC is an equilateral triangle with circum-radius = 12 cm

Now, O is the circumcentre of the triangle and it divides the median in the ratio 2:1

=> $$AO=\frac{2}{(2+1)}\times h$$

=> $$12=\frac{2}{3}\times h$$

=> $$h=12\times\frac{3}{2}$$

=> $$h=6\times3=18$$ cm

=> Ans - (C)

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