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Three circles are drawn, so that each circle is externally tangent to the other two circles. Each circle has a radius of $2.$ A triangle is then constructed, such that each side of the triangle is tangent to two circles, as shown below. Find the perimeter of the triangle.

 

 

[asy] unitsize(1 cm); draw(Circle(dir(90),sqrt(3)/2)); draw(Circle(dir(90 + 120),sqrt(3)/2)); draw(Circle(dir(90 + 240),sqrt(3)/2)); draw((1 + sqrt(3))*dir(90)--(1 + sqrt(3))*dir(90 + 120)--(1 + sqrt(3))*dir(90 + 240)--cycle); [/asy]

 Feb 9, 2020
 #1
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The perimeter of the triangle works out to 24 + 18*sqrt(3).

 Feb 10, 2020
 #2
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Thank you very much!

 Feb 10, 2020

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