+0  
 
0
45
2
avatar

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.

 


 

 Oct 7, 2020
 #2
avatar+111144 
+1

I have answered this before but I think I made a bigger job of it last time.

 

\(\tan30 = \frac{1}{\sqrt3}=\frac{2}{2\sqrt3}\\ so \\ x=2\sqrt3\\ so\\ perimeter = 3(4\sqrt3+4)\\ perimeter =12( \sqrt3+1)\;\;units\\ perimeter \approx 32.78\;\;units\\\)

 

 

 

LaTex

\tan30 = \frac{1}{\sqrt3}=\frac{2}{\sqrt3}\\
so \\
x=\frac{1}{2\sqrt3}=\frac{\sqrt3}{6}\\
so\\
perimeter = 3(\frac{2\sqrt3}{6}+4)\\
perimeter = \sqrt3+12\;\;units\\

 Oct 7, 2020

29 Online Users