CAT2 DS : Trying triangles (2) ...Someone pls respond

[gmatblr]

Question
In the diagram to the right, if arc ABC is a semicircle, what is the length of AC?
1. DC = 25/4
2. AD = 4

While proving the similarity of the two triangles , BD is shown as 5 in the solution . I do not understand how is BD 5 ,when nothing as such is stated in the Qn .Or if it is derived from the data , how do I get it?

I have undertood the solution part ,except for how is BD = 5.

THe below image is from the solution part ,where he states BD = 5

[guest]

Could someone respond to this question ? I came across the same problem and do not understand how the length of BD=5 ? Thanks

[jwinawer]

Well, I haven't seen this problem before and I do not know why you would need the length of DB if you are asked for the length of AC, which is the sum of AD and DC. Are you sure that the question is not what is the length of DB?

But in any case, if you did want to know the length of DB, here is how you would do it.

First, look at the diagram you attached: w and x must sum to 90 degrees. y and x must also sum to 90 degrees. this means that w = y. get rid of w and rename it y.

now we do the same for the other angle: x + y = 90 deg, and y + z= 90, so z = x. get rid of z and rename it x.

so now we have only 2 angles, x and y, in each of the two triangles. these are similar triangles (their angle measurements are the same). this also means their side lengths are proportional.

this means that the ratio of the side length opposite x (call it length X) to the side length opposite y (call it length Y) is the same in each triangle.

so for the left triangel X / Y = 4 / DB. for the right triangle, X / Y = DB / (25/4).

so 4/DB = DB/ (25/4).

now solve for DB and you will see that you get 5.

[yousuf_azim]

Dears,

What is the ans?

BR

[mithunsam]

Question should have been to find BD...

Answer should be C

[jnelson0612]

Question should have been to find BD...

Answer should be C

Concur. This question does not make sense as it is originally written.

[yousuf_azim]

Dears,

What is the ans?

BR

[tim]

did you read mithnusam's and jnelson's responses? the answer is C; please don't ask again..