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Triangles

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Triangles [#permalink] New post 21 Jan 2010, 11:44
Hi Experts,

Could anybody help me in understanding the reasoning and concept behind the following question:

Q: Which of the following can be the perimeter of a triangle inscribed in a circle with a radius of 1?
1. .001
2. .010
3. .100

a) 1 only
b) 3 only
c) 2 & 3 only
d) 1,2 & 3
e) not 1,2 or 3

Many thanks in anticipation.

-Amit
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Re: Triangles [#permalink] New post 21 Jan 2010, 14:41
Expert's post
D

You can choose any three points and draw a triangle. The closer these points the smaller triangle and its perimeter. So, perimeter can be almost 0. At the same time, perimeter cannot be essentially bigger than radius because such triangle cannot be inscribed. Let's say you build triangle with two sides almost 2r and third side - almost 0. This triangle will have perimeter ~ 4r or 4. Now we have range 4>P>0. Now you can see that P can be 0.001, 0.01 and 0.1
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Re: Triangles   [#permalink] 21 Jan 2010, 14:41
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