Geometry

ritula · Posted: Fri Sep 05, 2008 1:18 am Post subject: Geometry

PR and QR are two tangents drawn to a circle with centre O. What is angle PRQ?

(1) AnglePOQ = 120°
(2) PRO and ROQ are isosceles triangles.

OA is C but i dnt agree with it . please help

4meonly · Posted: Fri Sep 05, 2008 7:27 am Post subject:

hmmm
I have A

parallel_chase · Posted: Sat Sep 06, 2008 2:20 am Post subject: Re: Geometry

shahdevang87 · Posted: Sat Sep 06, 2008 4:32 am Post subject:

Hi parallel_chase,

Would you please explain in detail following points in explanation?

a)center angle120 , two sides isosceles means both the angles are 90 degree,

b)120/ 2= 60

Thanks

parallel_chase · Posted: Sat Sep 06, 2008 4:44 am Post subject:

sanjaylakhani · Posted: Sat Sep 06, 2008 4:56 am Post subject:

Angle formed by tangent and radius is always 90 deg

you do nt have to assume anything, in light of this D will be OA

ritula · Posted: Sun Sep 07, 2008 8:27 pm Post subject: Re:

Sanjay ,
Can u pls explain how statement 2 alone is also sufficient?

Vignesh.4384 · Posted: Mon Sep 08, 2008 11:27 pm Post subject:

i think it is D.
Please correct me if i am wrong.

ritula · Posted: Tue Sep 09, 2008 11:21 pm Post subject: Re:

Thanks a lot Vignesh for the wonderful explanation

mals24 · Posted: Wed Sep 10, 2008 4:36 am Post subject:

@ Vignesh.4384

the answer you get in both the statements is different

In st 1 you get PRQ = 60 degrees
In st 2 you get PRQ = 90 degrees

We should be getting an unique answer with both the statements for D to be correct.
I cant understand how st 2 can give an answer of PRQ = 60 degrees

Ian Stewart · Posted: Wed Sep 10, 2008 5:11 am Post subject:

The only way both statements can be true together is if R, P and Q are not points on the circle. We can certainly have a tangent line PR that touches the circle at a different point- A, say, and QR might touch the circle at B. Once you see this, it quickly becomes clear that neither statement is sufficient on its own. When you consider both statements together, there is a lot of work involved, unless I'm missing a trick. If POR is isosceles, we need to consider three possibilities- PO = PR, PO = OR and PR = OR- and we need to do the same for the other isosceles triangle. It's far too much work for a GMAT question, and I'm wondering if additional information was provided in the question (a diagram, perhaps?). Also curious about where the question is from.

ritula · Posted: Wed Sep 10, 2008 11:26 pm Post subject:

@ IAn
The source of this problem is www.tcyonline.com