Question

7. An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.
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Answer 1

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

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