Using a sextant, an angle can be measured between two objects ashore, the position of which is known. By plotting the intersection of two lines forming the horizontal sextant angles between the two objects, a circular position line can be drawn. Remember that all angles subtended by a chord in the same segment of a circle are equal.

Horizontal sextant angle (HSA).

The procedure for obtaining and plotting the position circle is as follows:

1. Connect the two navigational marks used for the horizontal sextant angle and measure the bearing of each from the other, ie
   Bearing between pos A and pos B = 350°/170° (T)
2. Deduct the HSA from 90°. This will give you the base angle of the triangle you are going to construct. Apply this angle to the bearings of the navigation marks and the resultant bearings, when plotted, will give you the centre of the position circle.Base angle = 90° – HSA = X°
   Bearing from pos A = 350° – X° = Y° (T)
   Bearing from pos B = 170° + X° = Z° (T)

   If the base angle is positive (HSA less than 90°), the centre of the circle will be on the observer’s side of the base line. If it is negative (HSA greater than 90°), the centre will be on the opposite side of the base line. If the angle is zero (HAS is equal to 90°), the centre of the circle will be on the mid point of the base line.

3. Add or subtract the “base” angle to or from the bearings of the two navigation marks.
4. Draw the two lines resulting from these bearings from the respective navigation marks. Where these lines intersect is the centre of the position circle.
5. Using the distance from the intersection point to either of the two navigation marks as
   radius, draw in the position circle.