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the inscribed triangle?

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by sanju09 » Sat Dec 28, 2013 10:41 pm
Triangle ABC is equilateral and BC = 1. Another equilateral triangle is to be inscribed in the triangle ABC so that each side of triangle ABC contains one vertex of the inscribed triangle. Which of the three points along BC in the figure may be used as a vertex of the inscribed triangle?
(A) y only
(B) y and z only
(C) x and z only
(D) x and y only
(E) x, y, and z
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by theCodeToGMAT » Sun Dec 29, 2013 9:03 am
Is the Answer [spoiler]{E}[/spoiler]?
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by sanju09 » Sun Dec 29, 2013 11:16 pm
theCodeToGMAT wrote:Is the Answer [spoiler]{E}[/spoiler]?
[spoiler]Prove that please![/spoiler]
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by theCodeToGMAT » Mon Dec 30, 2013 9:13 am
I don't know the logic behind the question; i solved it just by visual assumption..

Since ABC is equilateral triangle and we need to draw another equilateral triangle in it, the measurement gap, say cx/cy/cz, will imply to all sides..

So the figure becomes
Image

What is the correct Answer? Also, the explanation...

Thanks!
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by sanju09 » Tue Dec 31, 2013 2:53 am
theCodeToGMAT wrote:I don't know the logic behind the question; i solved it just by visual assumption..

Since ABC is equilateral triangle and we need to draw another equilateral triangle in it, the measurement gap, say cx/cy/cz, will imply to all sides..

So the figure becomes
Image

What is the correct Answer? Also, the explanation...

Thanks!
[spoiler](E) is the correct answer.[/spoiler]

If we pencil in from point x to a point that is ¾ of the approach from C to A and then pencil in from that point to a point that is ¾ of the approach from A to B, we'll get a triangle in which all the sides are the same length. This speculation works [spoiler]for each and every one[/spoiler] of the three points, hence the answer is [spoiler](E)[/spoiler].
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