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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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hfbamafan


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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Bunuel, can you expand on (2) showing that the triangles are similar?
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TooLong150
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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Bunuel
TooLong150
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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TooLong150
Bunuel
TooLong150
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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Zarrolou
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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