Perimeter of a triangle which circumscribes by 3 circles

AI Thread Summary
The discussion revolves around calculating the perimeter of an equilateral triangle that circumscribes three congruent circles, each with a radius of 1, which are externally tangent to each other. Participants suggest drawing lines connecting the centers of the circles to form a smaller triangle, which aids in understanding the relationship between the smaller and larger triangles. The user expresses difficulty in starting the problem and seeks hints rather than a complete solution. A key point raised is to determine the ratio of the perimeters of the larger triangle to the smaller triangle formed by the circle centers. This problem emphasizes the geometric relationships between tangents and the circles involved.
Paradiselovek
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Hello, I need help with this problem please (this is counted as large part of my grade so please hel) thank you

Problem:
Each of three congruent circles has radius 1, and each is externally tangent to the other two. An equilateral triangle circumsribes this configuration, so that each circle is tangent to two of the sides of the triangle. What is the perimeter of the equilateral triangle?

Here is my diagram. Please excuse me of my badly drawing scale TT

http://www.freeimagehosting.net/uploads/4a1d944fce.jpg
 
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Hi Paradiselovek! :smile:

Show us how far you get, and where you're stuck, and then we'll know how to help!

Hint: whenever you see tangent circles, draw the lines connecting their centres! (in this case, making a triangle) :wink:
 
tiny-tim said:
Hi Paradiselovek! :smile:

Show us how far you get, and where you're stuck, and then we'll know how to help!

Hint: whenever you see tangent circles, draw the lines connecting their centres! (in this case, making a triangle) :wink:

Well you see, I'm really stuck in this problem. I have no idea where to start to find the perimeter. I'm not asking for step by step but can you please help me by giving hints on those steps?thanks

here what I did like you said:
http://www.freeimagehosting.net/uploads/cccd0e11fa.jpg
 
One thing you can get easily is the perimeter of that inner triangle. Can see what the ratio of "large triangle to small triangle" must be?
 

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