What is the next step in completing this construction?

The next step would be the joint the point P with the two intersection points of the arcs on the circle.

Step-by-step explanation:

From the given graph it is clear that it represents the construction of tangents on the circle.

The steps for construction of tangents on a circle are:

1. Draw a line segment joining the point P to the center of the circle O.

2. Draw a perpendicular bisector of that segment.

3. Place the compass on the midpoint of the segment, stretch the compass upto the center and draw an arc across the circle.  Those arcs are point of tangency, i.e., J.

4. Now, draw the lines x connecting point p and the point of tangency.

Therefore the next step would be the joint the point P with the two intersection points of the arcs on the circle.

2 is the final ! : )