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In the above circle AB = 4, BC = 6, AC = 5 and AD = 6. What is the length of DE?

(A) 6 (B) 7.5 (C) 8 (D) 9 (E) 10

Attachment:

untitled.PNG [ 7.97 KiB | Viewed 13080 times ]

As all inscribed angles that subtend the same arc are equal then <BCD=<BED (as these angles subtend the arc BD) and <CBE=<CDE (as these angles subtend the arc CE). Also <BAC=<DAE. So triangles ABC and ADE are similar: in similar triangles, corresponding sides are all in the same proportion.

Bunuel I looked at the difference between the two sides since they had to be in same proportion. So just took 6/4 AD/AB = 3/2 and since BC=6 then DE=3/2(6) = 9 is this correct way of looking at it? Also the triangles are mirror images of each other so therefor side BA=AD? how do we know these are the angles that are corresponding.

Bunuel I looked at the difference between the two sides since they had to be in same proportion. So just took 6/4 AD/AB = 3/2 and since BC=6 then DE=3/2(6) = 9 is this correct way of looking at it? Also the triangles are mirror images of each other so therefor side BA=AD? how do we know these are the angles that are corresponding.

Because triangles ABC and ADE are similar their corresponding sides are all in the same proportion. Corresponding sides are the sides opposite the angles which are equal. For example as <BCA=<AED then the sides opposite them BA and AD are corresponding. So, in similar triangles the RATIO of corresponding sides are the same: BA/AD=BC/DE.

Next triangles are not congruent they are similar, so AB doesn't equal to AD (by the way stem gives AB = 4 and AD = 6).

In the above circle AB = 4, BC = 6, AC = 5 and AD = 6. What is the length of DE?

(A) 6 (B) 7.5 (C) 8 (D) 9 (E) 10

Attachment:

untitled.PNG

As all inscribed angles that subtend the same arc are equal then <BCD=<BED (as these angles subtend the arc BD) and <CBE=<CDE (as these angles subtend the arc CE). Also <BAC=<DAE. So triangles ABC and ADE are similar: in similar triangles, corresponding sides are all in the same proportion.

So, DE/BC=AD/AB --> DE/6=6/4 --> DE=9.

Answer: D.

Hi Bunuel,

I looked through the GMAT Club mathbook but i'm still having a hard time making the leap here:

What exactly does "subtend" mean? Why do you say that <BCD=<BED and not <BCD=<CDE (isn't it a transverse cutting a parallel line)?

In the above circle AB = 4, BC = 6, AC = 5 and AD = 6. What is the length of DE?

(A) 6 (B) 7.5 (C) 8 (D) 9 (E) 10

Attachment:

The attachment untitled.PNG is no longer available

As all inscribed angles that subtend the same arc are equal then <BCD=<BED (as these angles subtend the arc BD) and <CBE=<CDE (as these angles subtend the arc CE). Also <BAC=<DAE. So triangles ABC and ADE are similar: in similar triangles, corresponding sides are all in the same proportion.

So, DE/BC=AD/AB --> DE/6=6/4 --> DE=9.

Answer: D.

Hi Bunuel,

I looked through the GMAT Club mathbook but i'm still having a hard time making the leap here:

What exactly does "subtend" mean? Why do you say that <BCD=<BED and not <BCD=<CDE (isn't it a transverse cutting a parallel line)?

Thanks!

Angles BCD and BED are based on minor arc BD, thus they are equal:

Re: In the above circle AB = 4, BC = 6, AC = 5 and AD = 6. What [#permalink]

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20 Feb 2016, 11:23

angle A is at the intersection of two lines..thus, the angle A of the both triangles must be the same. somewhere I read that the angles of the cord when represented on the circle are the same...so triangles must be similar. AD is similar to AB. the multiplier factor thus must be 6/4 or 3/2. now, we know that BC is 6. ED will be 6*3/2 or 9.