Question

An equilateral triangle is inscribed in a circle of radius 6 cm. Find its side

Answer 1

Suppose you have a triangle ABC. Let AD be the median where D lies on BC. Since it is an equilateral triangle, D will be the mid-point of side BC.
Now, for the time being, let us assume that the length of each side of the equilateral triangle is x.
=> AD = x/2
Also we know that all the angles of an equilateral triangle measure 60 degrees. Using trigonometry, sin60 = AD/AB
=> sqrt(3)/2 = AD/AB
=> AD = AB * sqrt(3)/2
We also know that the centroid of an equilateral triangle divides the median in two parts in the ratio 2:1 and bigger part of that median is the centre of the circle.
So the bigger part of the median (or the radius of the circle is)
        2/3 √(3)/2 * AB
 i.e., x/sqrt(3)   [AB=x]
i.e.,  6/sqrt(3)   [x=6, which is given]
=2√3

Answer 2

Step-by-step explanation:

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