The measure of the arc would be twice is inscribed angle and so the measure of arc PO would be twice of its inscribed angle which is 35 degrees. So the measure of Po is 70 degrees.
It is given that PQ is parallel to OR and so angle QPR would be equal to angle PRO and therefore measure if arc QR would also be 70 degrees.
Because OR is the diameter we know that the measure of arc OR is 180 degrees.
OP is 70 degrees and QR is 70 degrees so the remaining measure of arc PQ would be 40 degrees(180-70-70)
Length of the arc PQ would be 40/360*2(pie)(r) = 1/9 * 18(pie)=2(pie)
So the answer is choice A
GMATPrep Geometry Problem Lenght Arc Parallel lines
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