Assume centre of the circle to be point C.

Since angle ORP = \(35^{\circ}\) , angle OCP will be = \(70^{\circ}\)

Note: This follows from the circle property that an inscribed angle (angle ORP in our case) is exactly half the corresponding central angle (angle OCP in our case).

Now, we can calculate the length of arc OP :

Length of arc OP = (angle OCP)*(radius of circle) = \(\frac{7\pi}{18}*9\) = \(\frac{7\pi}{2}\)

Note: An angle of \(70^{\circ}\) corresponds to \(\frac{7\pi}{18}\) radians.

Also, since chord PQ is parallel to the diameter, arc OP must be equal to arc QR.

Therefore, total length of arc OP + QR = \(\frac{7\pi}{2}+\frac{7\pi}{2}\) = \(7\pi\)

Now, length of arc PQ will be = half the circumference of the circle - combined length of arcs OP and QR

Half the circumference of the circle = \(\pi*r\) = \(9\pi\)

Thus length of arc PQ = \(9\pi - 7\pi\) = \(2\pi\)

Answer : A
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