A circle has a radius of 6 in. Find the area of its circumscribed equilateral triangles.

A circle has a radius of 6 in. The circumscribed equilateral triangle will have an area of:

Area = 27√3

Explanation:

Length of a side of an equilateral triangle inscribed in a circle = r√3, where r is the radius of the circle

Therefore, Area = √3 a24

a=6√3

Note: how to get the above relation?

asinA = csinC

⇒c=a⋅ (sinCsinA) = 6⋅ (sin120sin30) = 6√3