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In the figure to the right, if point C is the center of the

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tweakxc03
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In the figure to the right, if point C is the center of the [#permalink] New post  17 Sep 2009, 08:23
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In the figure to the right, if point C is the center of the circle and DB = 7, what is the length of DE?

(1) x = 60°

(2) DE || CA

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Zarrolou
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  04 May 2013, 10:56
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The correct answer is B.

Using similar triangles properties we can solve the question.

\(\frac{BC}{DB}=\frac{AC}{DE}\) \(\frac{3.5}{7}=\frac{3.5}{DE}\)

What you say (that A is sufficient) is not correct; you are assuming that DE || CA in your solution
Take a look at the picture, should be clear enough

BTW "we can use Tan": in GMAT you don't need trigonometry
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deepakraam
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  17 Sep 2009, 10:02
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I wud go with option B.

Line joining the midpoint and parallel to the third side will be half the length of the third side.So statement 2 states it is parallel to the third side.So DE = 7 cm.

I wud go with option B
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  07 Dec 2013, 17:10
So what is the answer??

1) Obviously A is out

2) But how is B right?

1&2 How can we determine length?

This is confusing!
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  08 Dec 2013, 06:56
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hfbamafan wrote:

In the figure to the right, if point C is the center of the circle and DB = 7, what is the length of DE?

(1) x = 60°

(2) DE || CA


So what is the answer??

1) Obviously A is out

2) But how is B right?

1&2 How can we determine length?

This is confusing!


From (2) it follows that triangles DEB and CAB are similar, which means that the ratio of their corresponding sides is the same: DE/CA = DB/CB. Since CA=CB=radius=DB/2=3.5, then DE/3.5 = 7/3.5 --> DE=7.

Hope it's clear.
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  19 Dec 2013, 23:51
Bunuel, can you expand on (2) showing that the triangles are similar?
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  20 Dec 2013, 00:33
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TooLong150 wrote:
Bunuel, can you expand on (2) showing that the triangles are similar?


We know for (2) that DEB and CAB are similar because they have all 3 angles equal: they have the same angle B, angle D equals to angle C (since DE || CA) and thus the remaining angles are also equal.

Hope it's clear.
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  20 Dec 2013, 00:48
Bunuel wrote:
TooLong150 wrote:
Bunuel, can you expand on (2) showing that the triangles are similar?


We know for (2) that DEB and CAB are similar because they have all 3 angles equal: they have the same angle B, angle D equals to angle C (since DE || CA) and thus the remaining angles are also equal.

Hope it's clear.


Please explain how angle EDB = angle ACB. I still can't see it.
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  20 Dec 2013, 00:55
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TooLong150 wrote:
Bunuel wrote:
TooLong150 wrote:
Bunuel, can you expand on (2) showing that the triangles are similar?


We know for (2) that DEB and CAB are similar because they have all 3 angles equal: they have the same angle B, angle D equals to angle C (since DE || CA) and thus the remaining angles are also equal.

Hope it's clear.


Please explain how angle EDB = angle ACB. I still can't see it.


That's because DE is parallel to CA.
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Re: In the figure to the right, if point C is the center of the [#permalink] New post  28 Dec 2023, 01:27
Zarrolou wrote:
The correct answer is B.

Using similar triangles properties we can solve the question.

\(\frac{BC}{DB}=\frac{AC}{DE}\) \(\frac{3.5}{7}=\frac{3.5}{DE}\)

What you say (that A is sufficient) is not correct; you are assuming that DE || CA in your solution
Take a look at the picture, should be clear enough

BTW "we can use Tan": in GMAT you don't need trigonometry


Sorry do you mind elaborating why A is not sufficient? Both larger and smaller triangles have the same angles (60/60/60). Thanks
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Re: In the figure to the right, if point C is the center of the [#permalink]
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