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# If B is the midpoint of AC, what is the length of BE?

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If B is the midpoint of AC, what is the length of BE? [#permalink]  05 Feb 2012, 18:09
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If B is the midpoint of AC, what is the length of BE?

(1) <BAE = 60 degrees

(2) CD = $$\sqrt{12}$$
[Reveal] Spoiler: OA

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Re: Length of BE [#permalink]  05 Feb 2012, 18:14
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If B is the midpoint of AC, what is the length of BE?

As angle E=Angle D then BE||CD. Now as B is the midpoint of AC and BE||CD then BE becomes a midsegment (a line segment joining the midpoints of two sides of a triangle). The property of midsegemnt: the midsegment is always half the length of the third side. So 2BE=CD.

(1) <BAE = 60 degrees --> triangles BAE and CAD are 30-60-90 triangles where BE is a midsegment. We know only angles but not the lengths, so can not find BE. Not sufficient.

(2) CD = $$\sqrt{12}$$ --> as 2BE=CD then $$BE=\frac{CD}{2}=\sqrt{3}$$. Sufficient.

Hope it's clear.
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Status: Finally Done. Admitted in Kellogg for 2015 intake
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Re: Length of BE [#permalink]  05 Feb 2012, 18:15
You are a legend buddy. Top explanation.
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink]  25 May 2013, 03:42
Expert's post
Bumping for review and further discussion.
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink]  05 Aug 2013, 17:57
Another EASIER way of looking at the problem
(1) we know the angle but not length of any side. Insufficient. Proceed to D

(2)CD=Root 12
Use property of similarity and we get that triangle ABC is similar to triangle ACD

AC/AB=DC/BE

As B is a midpoint of AC we get 2AB=AC

2AB/AB=Root12/BE

BE=Root12/2
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink]  05 Aug 2013, 17:59
typing mistake above. "proceed to 2" and not "proceed to D"
sorry.
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink]  05 Aug 2013, 22:18
enigma123 wrote:
Attachment:
doubletr_q1.png
If B is the midpoint of AC, what is the length of BE?

(1) <BAE = 60 degrees

(2) CD = $$\sqrt{12}$$

st(2), BE II CD and B is the midpoint.
so BE = 1/2 CD = fixed value.
st(1) provides no fixed value, so insufficient.
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink]  16 Sep 2014, 11:26
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: If B is the midpoint of AC, what is the length of BE?   [#permalink] 16 Sep 2014, 11:26
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