An equilateral triangle of side 9 cm is inscribed in a circle. Find the radius of the circle.
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, we have
AB2 = AD2 + DB2
92 = AD2 + DB2
AD = cm
Therefore,
Radius = AG = AD
= 3 cm