For setting out a simple curve, using two theodolites.

ANS:E - none of these.

Answer E is correct.

Option A, B, C are linear methods of setting out a curve. And option D is an instrumental method but in Rankine's method of deflection angles, one theodolite and one tape are used to measure angle and length respectively. In two theodolite method, curves are staked out by angular measurements only. Accuracy attained in this method is quite high. Thus, the method is used when higher accuracy is required and when the topography is rough or field condition is difficult.

Under "Fundamental Geometry of Circular Curve";

The underlying principle of this method is that the deflection angle between a tangent (at any point on a circle) and a chord is equal to the angle which the chord subtends in the alternate segment. The angle between tangent and chord is angle made by tangent in opposite segment.