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If BC = BD, what is the length of BC?

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ind23
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If BC = BD, what is the length of BC? [#permalink] New post   12 Apr 2014, 11:27
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If BC = BD, what is the length of BC?

(1) x = 30
(2) AD = 1


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If BC = BD, what is the length of BC? [#permalink] New post   13 Apr 2014, 06:56
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If BC = BD, what is the length of BC?

Look at the diagram below:

As you can see fro the stem we can get that \(\angle{DBA} \angle{DAB}=2x\), from which it follows that AD = BD, thus AD = BD = BC.

(1) x = 30. This statement must be insufficient, because we are asked to find the length and all we know are angles. Not sufficient

(2) AD = 1 --> we know that AD = BC, thus BC = 1. Sufficient.

Answer: B.

Hope it's clear.

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If BC = BD, what is the length of BC? [#permalink] New post   12 Apr 2014, 16:21
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ind23 wrote:
If BC = BD, what is the length of BC?

1) x = 30
2) AD = 1


An easy one..just assign x to Angle-BDC & Angle-BCD..keep on applying the Sum of all angles is 180 rule until you get all the angles in terms of x
You get
-->Angle DAB = Angle DBA = 2x
--> AD = BD

As BD=BC
--> AD=BD=BC=1
As given in B
So B it is
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Re: If BC = BD, what is the length of BC? [#permalink] New post   10 Mar 2021, 22:03
Bunuel wrote:

If BC = BD, what is the length of BC?

Look at the diagram below:

As you can see fro the stem we can get that \(\angle{DBA} \angle{DAB}=2x\), from which it follows that AD = BD, thus AD = BD = BC.

(1) x = 30. This statement must be insufficient, because we are asked to find the length and all we know are angles. Not sufficient

(2) AD = 1 --> we know that AD = BC, thus BC = 1. Sufficient.

Answer: B.

Hope it's clear.

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Attachment:
Untitled.png


Totally follow the logic except one thing: AD = BD = BC. Why does this hold true? If 2x opposes the side that is length 1, shouldn't the length of the side that opposes x be 1/2? Given the way the question is set up, I can see that all sides necessarily must equal 1, but I just find it weird that this holds for different angles...
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Re: If BC = BD, what is the length of BC? [#permalink] New post   28 Oct 2023, 12:31
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Re: If BC = BD, what is the length of BC? [#permalink]
28 Oct 2023, 12:31
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