Question

An equilateral triangle is inscribed in the circle having the radius ‘r’ then its side is

Answer 1

Answer:

r√3

Step-by-step explanation:

In an equilateral triangle the circumcentre coincides with the centroid. Centroid divides the median in 2:1 ratio so the circumcentre. Let the length of the side of the equilateral triangle be a. And the given circle has side r. Length of median can be found by pythagoras rule applied to right triangle with hypotenuse a and one side a/2.

Observe the provided picture, you can see a right-angled triangle with sides  r, a/2 , a/2√3  ( one side is a/2 because a median bisects its side, another side is a/2√3 because centroid (also circumcentre since it is an equilateral triangle) divides median in 2:1 ratio)

By Pythagoras theorem

r² = (a/2)² + (a/2√3)²

r² = a²/4 + a²/12

r² = 4a²/12

a²=3r²

a=r√3.

Mission accomplished