Archit3110 wrote:
GMATPrepNowgiving a try
I solved the question using given answer choices for x
let side OD = a
so radius of circle = 5+a
for ∆ ABD we can say
(√24)^2= ( x)^2+ ( 5+2a)^2 ------(1)
substituting values of x we can clearly see that options c,d,e wont be valid as in that case the relation (1) wont be valid
amongst a & b
I checked with x=\(\sqrt{15}\) & \(2\sqrt{5}\) ; there in value of a is coming out to be -ve...
I am not sure whether which one would be correct.. as value of a is coming an integer for option A ( -4,-1) and fraction for option B ( -7/2,-3/2)
IMO A ;
GMATPrepNow wrote:
O is the center of the circle. If line segment DC has length 5, and side AB has length \(\sqrt{24}\), what is the length of x?
A) \(\sqrt{15}\)
B) \(2\sqrt{5}\)
C) \(2\sqrt{6}\)
D) \(\sqrt{30}\)
E) \(6\)
Aside: I posted a nearly-identical question a few minutes ago, and realized there was a flaw. So, I deleted the question and posted this corrected version.
Sorry to those who attempted my first post. This is a great approach. In fact, if I had used that approach, I would have seen that the diagram I created cannot exist in our Universe.
When creating the question, I used the similar triangles approach used by
Dillesh4096 and
firas92 asmd and my calculations yielded an answer of \(\sqrt{15}\) (answer choice A)
However, this means my diagram makes no sense whatsoever.
Notice that, if \(x=\sqrt{15}\), then we can use the Pythagorean Theorem to see that side BC has length \(\sqrt{40}\)
And all of this means that side AC has length 8
In other words, the diameter of the circle is 8, which means the radius is 4.
This is where things get ugly. If the radius is 4, how can side DC = 5?
Ughh!!!!!!
That said, the above solutions are great/valid.
The only issue is that diagram is nonsensical.
My apologies.
Kudos for everyone!!!
Cheers,
Brent
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