Geometry

Question

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 · Answer

hmmm I have A

parallel_chase · Answer

ritula wrote: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

I guess you are assuming that every tangent drawn to the circle makes a 90 degree angle.
One cannot simply assume that, when it is not mentioned.

Statement I

angle formed at the center of the circle is 120.

We dont know anything about the other 2 tangents or their angles.

Insufficient.

Statement II

two opposite triangles are isosceles triangles, we dont know anything about the other angle formed at the center, therefore Insufficient.

Combining I & II

center angle120 , two sides isosceles means both the angles are 60 degree,

120/ 2= 60

In two triangles we 60-60 formation, therefore angle PRQ=60

Sufficient.

Hence C is the answer.

shahdevang87 · Answer

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 · Answer

shahdevang87 wrote: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

I actually made a mistake, i have revised my above post.

"two sides isosceles means both the angles are 90 degree" this means the angle is 60 degrees not 90 thats a typo

120/ 2= 60

this is done to divide the center angle into two equal parts since the two triangles share the same angle at the center.

Hope its clear, Let me know if you have any doubts.

sanjaylakhani · Answer

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 · Answer

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

sanjaylakhani wrote: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

Vignesh.4384 · Answer

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

ritula · Answer

Thanks a lot Vignesh for the wonderful explanation Vignesh.4384 wrote:i think it is D. Please correct me if i am wrong.

mals24 · Answer

@ 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 · Answer

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 · Answer

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

Choose how you want to prepare

Get Ready for GMAT Test Day Faster with Live Online Classes

Target Test Prep EA OnDemand

Target Test Prep GMAT OnDemand

Geometry

Re: Geometry

Re:

Re:

GMAT/MBA Expert

Chicago Booth

GMAT Course Reviews

Admissions Consulting Reviews

FREE GMAT PREP RESOURCES

GMAT PREP DEAL TRACKER