Perimeter of a triangle which circumscribes by 3 circles

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Homework Help Overview

The problem involves finding the perimeter of an equilateral triangle that circumscribes three congruent circles, each with a radius of 1, which are externally tangent to each other. The setup requires understanding the geometric relationships between the circles and the triangle.

Discussion Character

  • Exploratory, Assumption checking, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the importance of visualizing the problem by drawing the lines connecting the centers of the circles. There is a focus on understanding the relationship between the triangle and the circles, particularly regarding the ratios of the triangles formed.

Discussion Status

The discussion is ongoing, with participants providing hints and encouraging the original poster to explore their understanding further. Some guidance has been offered regarding the inner triangle formed by the centers of the circles, but no consensus or complete solution has been reached.

Contextual Notes

The original poster expresses concern about the problem's significance to their grade and seeks assistance without requesting complete solutions. There is an emphasis on providing hints rather than direct answers.

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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