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.

Guest Oct 7, 2020

#2**+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\\

Melody Oct 7, 2020