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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, as shown below. Find the perimeter of the triangle.

 Jul 29, 2020
edited by Weiart000  Jul 29, 2020
 #1
avatar+1039 
+7

what is the radius of the circle? I think it got cut off.

 Jul 29, 2020
 #2
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Oh whoops! The radius of the circles are 2. Thanks for the reminder!

Weiart000  Jul 29, 2020
 #5
avatar+1039 
+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! wink)

ilorty  Jul 29, 2020
edited by ilorty  Jul 29, 2020
 #6
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+2

Wow! Great job on my challenge! That is correct, and your way to do solve it was perfect!

Weiart000  Jul 29, 2020
 #3
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0

This doesn't make sense...

You didnt tell us what the radius was.

"Three circles are drawn, so that each circle is externally tangent to the other two circles. Each circle has a radius of (where is it???). A

 Jul 29, 2020
 #4
avatar+232 
+1

Yeah, I told "ilorty" that the radius was 2 for all of the circles.

Weiart000  Jul 29, 2020

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