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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.

 

Here is the link to the image:

https://latex.artofproblemsolving.com/5/6/c/56c2e4a15c4c4654523f9b7ac15535647d8bce47.png

 Aug 11, 2020
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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.

 

This is an equilateral triangle.      r = 2 units      Perimeter  P = ?

 

P = 3[ 2( 2 / tan30º) + 2r]   

 

 Aug 11, 2020

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