33 cm

ABC is an equilateral triangle.

AB = BC = CA = 9 cm

<BOC = 2<BAC

= 2× 60°

= 120°

OD bisects BC perpendicularly.

In ∆BOC ,

<OBD = 30° ,

BD = BC/2 = 9/2 cm

\begin{lgathered}cos 30\degree = \frac{BD}{OB}\\=\frac{\frac{9}{2}}{r}\end{lgathered}

Therefore, 33 cm

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Answer:

Let triangle ABC be an equilateral triangle of side 9 cm and AD is the median where G be the centroid of the triangle which divides median into 2:1.

GD is perpendicular to BC.

In right triangle ADB,

AD2 + DB2 = AB2 where AB = 9 cm and BD = 4.5 cm

AD2 + (9/2)2 = 92

AD2 = 81 - 81/4 = 243/4

AD = 9√3/2

Radius = 2/3 AD = 2/3 × 9√3/2 = 3√3 cm

Step-by-step explanation:

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