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

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enigma123
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If B is the midpoint of AC, what is the length of BE? [#permalink] New post   05 Feb 2012, 19:09
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If B is the midpoint of AC, what is the length of BE?


(1) <BAE = 60 degrees

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


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Re: If B is the midpoint of AC, what is the length of BE? [#permalink] New post   05 Feb 2012, 19:14
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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.

Answer: B.

Hope it's clear.
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink] New post   05 Feb 2012, 19:15
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] New post   05 Aug 2013, 18:57
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] New post   05 Aug 2013, 18:59
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] New post   05 Aug 2013, 23:18
enigma123 wrote:
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If B is the midpoint of AC, what is the length of BE?

(1) <BAE = 60 degrees

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


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.
Answer (B)
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink] New post   11 Aug 2020, 04:56
enigma123 wrote:

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

(1) <BAE = 60 degrees
(2) CD = \(\sqrt{12}\)


(1) insufic

(2) sufic

CD/BE=AD/AE
√12/y=x/(x/2)
√12/y=2
y=√12/2=√3

Ans (B)
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink] New post   09 Dec 2023, 20:00
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Re: If B is the midpoint of AC, what is the length of BE? [#permalink]
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