MGMAT CAT: Triangles

[aaa]

http://www.manhattangmat.com/OnlineExam ... ID=1280045

Please refer to the link above for the diagram.
How do you know that ac is 3.5 in answer b? I am assuming it's bc angle x is 60. But how do you know angle x is 60? Thanks


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

For GMAT triangle problems, one useful tool is the similar triangle strategy. Triangles are defined as similar if all their corresponding angles are equal or if the lengths of their corresponding sides have the same ratios.

(1) INSUFFICIENT: Just knowing that x = 60° tells us nothing about triangle EDB. To illustrate, note that the exact location of point E is still unknown. Point E could be very close to the circle, making DE relatively short in length. However, point E could be quite far away from the circle, making DE relatively long in length. We cannot determine the length of DE with certainty.

(2) SUFFICIENT: If DE is parallel to CA, then (angle EDB) = (angle ACB) = x. Triangles EBD and ABC also share the angle ABC, which of course has the same measurement in each triangle. Thus, triangles EBD and ABC have two angles with identical measurements. Once you find that triangles have 2 equal angles, you know that the third angle in the two triangles must also be equal, since the sum of the angles in a triangle is 180°.

So, triangles EBD and ABC are similar. This means that their corresponding sides must be in proportion:

CB/DB = AC/DE
radius/diameter = radius/DE
3.5/7 = 3.5/DE
Therefore, DE = diameter = 7.

The correct answer is B.



You must select an

[StaceyKoprince]

Unfortunately, a link to your practice center won't work - people would have to know your username and password to access your account. (And I can't either, since I don't have access to your info.)

People generally take screen shots and use a photo hosting service to upload the image.
See here for an example: http://www.manhattangmat.com/forums/gmatprep-17-of-37-practice-test-1-t1054.html

The particular service used in the above example is http://postimage.org/

[claudia.baptista.fernandes]

I actually have the same question, in this exercice how do you know in 2) that the triangle is equilateral without knowing the value of x?

[tim]

post an image and then we can help you further..

[sachin.w]

Here's the image:
http://postimage.org/image/hvvg8v1in/

My Question is , nowhere is it mentioned that DBE is a triangle
Figure DBAE could just be a polygon if we were to extend E further..

And if it is not a traingle, E would be the answer.

[RonPurewal]

My Question is , nowhere is it mentioned that DBE is a triangle
Figure DBAE could just be a polygon if we were to extend E further..

thanks for posting the picture.

1/
single letters (in geometric diagrams) are POINTS. there is no such thing as "extending" a point.

2/
even if a diagram is not to scale, you can still trust that (a) straight lines represent straight lines, (b) points are actually connected as shown, and (c) intersection points represent intersection points.

[sachin.w]

Thanks a lot for the reply. It helped.

[RonPurewal]

Thanks a lot for the reply. It helped.

you're welcome.

[cleo.cheung]

I have a further follow up:

The answer to this question says: "Once you find that triangles have 2 equal angles, you know that the third angle in the two triangles must also be equal, since the sum of the angles in a triangle is 180°."

How do you know that if two different triangles (triangle EBD and ABC) have 2 equal angles (i.e. angle EDB = ACB and angle EBD = ABC); that those 2 sets of equal angles equal each other? In other words, not sure how you reach the conclusion that EDB = ACB = EBD = ABC? What if angle EDB = ACB = 70 degrees and angle EBD = ABC = 60?

[tim]

If I’m interpreting your question correctly, it won’t matter, because the theorem will still hold. If EDB=ACB=70 and EBD=ABC=60, you’ll still have DEB=CAB=50, just as the theorem predicts. Please let us know if you are actually asking a different question so we can help you with that..

[arpanchandra]

Hi MGMAT,

I have a small question regarding option 1: x = 60 (degree).

According to me:
In traingle ACB
C is the centre of circle with A and B points on circle
that means
AC=BC (both radius)
therefore triangle is isoceles.
and in this triangle one angle is 60(degree)....whaich makes this triangle an equilateral triangle.
So, in triangle ACB and triangle EDB
comman angle B (makes them similar)
therefore
BC/BD=AC/ED

3.5/7=3.5/ED

SO, ED=7

which makes
Statement (1) sufficient.

Please let me know where I am going wrong?

[arpanchandra]

OK.
I got the answer:
We need minimum of two angles to make triangle similar.

[RonPurewal]

OK.
I got the answer:
We need minimum of two angles to make triangle similar.

always nice when posters answer their own questions!
(: