Perimeter of a triangle which circumscribes by 3 circles

Paradiselovek · Apr 22, 2009

Hello, I need help with this problem plz (this is counted as large part of my grade so plz 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

tiny-tim · Apr 23, 2009

Hi Paradiselovek!

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)

Paradiselovek · Apr 23, 2009

tiny-tim said: ↑

Hi Paradiselovek!

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)

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

HallsofIvy · Apr 23, 2009

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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Perimeter of a triangle which circumscribes by 3 circles

Paradiselovek

tiny-tim

Paradiselovek

HallsofIvy

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