To find the length of minor arc PQ, we need to get the angle extended by the arc at the center of the circle. Name the center as C. We need to find the angle PCQ and substitute in the formula (θ/360)*2πr where θ is the angle subtended by the arc at the center.

Step 1:Since the lines OR and PQ are parallel and Angle ORP is 35 degrees, as per alternate angles rule, angle RPQ is 35 degrees.

Step 2:Draw a line from P to C. Line PC is equal to CR, which is the radius i.e 9. Now consider the triangle RPC. In this triangle, 2 sides are equal PC and CR and the angle CRP is 35 degrees. As per the rules of isosceles triangle, angle RPC must also be 35 degrees.

So, the total angle CPQ is 70 degrees.

Step 3:Draw a line from Q to C. So, line PC is equal to line QC. If angle CPQ is 70 degrees, then angle PQC will also be 70 degrees.

Finally, angle PCQ is 180-140 = 40 degrees

Step 4:Substitute 40 in the formula (θ/360)*2πr = (40/360)*(2*π*9) = 2π

The answer is (A)--== Message from the GMAT Club Team ==--

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