Triangle ABC is an equilateral triangle and O is the center of its inscribed circle. If the area of the circle is \(4\pi\) sq cm, what is the area, in square centimeters, of triangle ABC? Express your answer in simplest radical form

tertre
Mar 12, 2018

#1**+1 **

The radius of the circle can be found as

4pi = pi*r^2 ⇒ r = 2

(1/2) of the side, m, of the triangle can be found as

2 / sin(30) = m / sin( 60)

2sin(60) / sin( 30) = m

4 * sin 60 =

4 *√3/2 = m = 2√3

So.....the side of the triangle is twice this = 4√3 = √48

And the area is

(1/2)( √48)^2 sin 60 =

24 * √3 / 2

12√3 cm^2

CPhill
Mar 12, 2018