Hi Naveen,
Since PQ and OR are parallel, then we can think of PR as a transversal. When two parallel lines are cut by a transversal (a third line), then all of the acute angles are equal, and all of the obtuse angles are equal.
Following this rule, since angle PRO = 35, then angle QPR = 35.
Angle QPR is called an "inscribed angle" since it's vertex is on the circumference of the circle, and arc QR is called the "intercepted arc".
Easier GMAT questions will put the "inscribed angle"'s vertex at the center of the circle (called a "central angle"). If we know the "central angle" we can usually solve for the arc length using a proportion, since the "central angle" is always a fraction of 360 degrees.
To find the "central angle" of 35 degrees, all we have to do is double it. So the "central angle" that corresponds to the "intercepted arc" has a measure of 70.
Now we can set up a proportion using our knowledge of part/whole:
70/360 = arc QR / 2*pi*r
Again, we can do this because there are 360 degrees total around the centerpoint of a circle, and any arc of a circle can be expressed as a fraction of the circle's total circumference (found by the expression 2*pi*r).
Since the diameter is 18, the radius is 9. Plugging that in:
70/360 = arcQR / 18pi
Now we can cross-multiply to solve:
(70)(18pi) = (360)(arcQR)
1260pi = (360)(arcQR)
3.5pi = arcQR
The answer is C.
