An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.

Answer

`3 sqrt(3) cm`

Explanation

Let `Delta ABC` be an equilateral triangle of side 9cm. Let AD be one of its medians
Then, `AD _|_ BC` and` BD = 4.5cm`.
`:. AD = sqrt(AB^(2) -BD^(2))=sqrt((9)^(2)-((9)/(2))^(2))cm= (9sqrt(3))/(2) cm`
In and equilateral triangle, the centroid and circumcentre coincide and `AG : GD = 2:1`
`:. ` radius ` = AG (2)/(3) AD ((2)/(3) xx (9sqrt(3))/(2)) cm = 3 sqrt (3) cm`