Manhattan FlashCards -Geometry

[tarunchavi]

GMAT flashcards can be downloaded or reviewed online. I found a slight difference between the two versions.

So, request to refer to online version for my querry.

Flashcard nos Q 8/23 under GEOmetry section.

P, S, R are points on the circle, wheras O is a point inside the circle. Angle PSR is an inscribed angle with 30degrees. Is it necessary that if the angle POR is 60degrees, then O is the center of the circle?

I dont think so (just a gut feeling) as I can always find multiple points within a circle which will form a 60degree angle with S and R.

I think, the converse is true. If the central angle is x degrees (formed using the centre), then the inscribed angle is x/2.

So, in my view, the answer to the flashcard question is INsufficient.

cheers.

[tim]

You are correct. Any point Q on the circle running through O, P, and R will also give you an angle PQR of 60 degrees if POR is 60 degrees. The flash card gives a great explanation for how we know O is 60 if it is a central angle, but it assumes without justification that the converse is true. Good catch!