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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. Find the perimeter of the triangle.

 Dec 14, 2020
edited by Guest  Dec 14, 2020
 #1
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Using 30-60-90 triangles, the side length of the equilateral triangle is 4*sqrt(3).

 

Area of equilateral triangle = sqrt(3)/4*(side length)^2

= sqrt(3)/4*(4*sqrt(3))^2

= 12*sqrt(3)

 Dec 14, 2020
 #2
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The perimeter of a triangle      P = 12√3 + 12

jugoslav  Dec 14, 2020

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