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.

Weiart000 Jul 29, 2020

#1

#5**+9 **

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! )

ilorty
Jul 29, 2020