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.
Okay! So, first, you need to draw perpendicular lines from the radii to the triangle like this:
https://ibb.co/FJ6m67v (picture is not mine)
Since the triangle is a triangle, and the lines are perpendicular, you have created a 30-60-90 triangle. Using the 30-60-90 side lengths, we can get AG = 2root{3}. Same thing with HC, as they are symetrical.
DGHF is a rectangle, which means GH = 2+2 = 4
So AC = 4root(3) + 4. => I got 4root(3) from multiplying 2root(3) by 2 (there are two per side), and 4 from the value we got before .
Multiply that by 3, and you get 12root(3)+12 for your answer!
(Please correct me if I am wrong. I'm not the best at geometry! )