Question

an equilateral triangle is inscribed in a circle if its one side is 9 cm find the radius of a circle

Answer 1

Answer,

Let ABC be an equilateral triangle of side 9 cm
Let, AD be one of its medians and G be the centroids of the triangle ABC

Then,

AG: GD = 2: 1

We know that,

In an equilateral triangle centroid coincides with the circumcentre

Therefore,

G is the centre of the circumference with circum radius GA

Also, G is the centre and GD is perpendicular to BC

Therefore,

In right triangle ADB,

AB² = AD ²+ DB²

9²= AD²+ DB²

AD = 9√3/2 cm

Therefore,

Radius = AG = 2/3 AD

= 3√3 cm

Thanks!

Answer 2

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Let ABC be an equilateral triangle of side 9 cm

Let, AD be one of its medians and G be the centroids of the triangle ABC

Then,

AG: GD = 2: 1

We know that,

In an equilateral triangle centroid coincides with the circumcentre

Therefore,

G is the centre of the circumference with circum radius GA

Also, G is the centre and GD is perpendicular to BC

Therefore,

In right triangle ADB,

AB² = AD ²+ DB²

9²= AD²+ DB²

AD = 9√3/2 cm

Therefore,

Radius = AG = 2/3 AD

= 3√3 cm

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