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# Help! I need help! Geometry.....

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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

tertre  Mar 12, 2018
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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

CPhill  Mar 12, 2018