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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

 Mar 12, 2018
 #1
avatar+98123 
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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

 

 

cool cool cool

 Mar 12, 2018

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