Two Diverging Lines With Their Intersect Inside A Circle

Steps

1. Draw the perpendicular line f to the given line p₂ so that it passes through the centre of the given circle (E). The points G and J are the intersections of the perpendicular line f with the given circle.
2. Draw the perpendicular line g to the given line p₁ so that it passes through the centre of the given circle (E). Points H and I are the intersections of the perpendicular line g with the given circle.
3. Draw 4 lines where each line passes through one of the constructed intersections. Each of these lines is also perpendicular to either line f or g, depending on which of these the constructed intersection lies on.
4. The intersections of these 4 constructed lines are named K, L, M, and N.
5. Name the intersection of the given lines O.
6. Construct the line OL and name it l.
7. Name the intersections of the given circle and line l P and Q.
8. Construct the axes of the angles between the given lines.
9. Construct the line EP. Name the intersection of the line EP and the angle axis S₁. The S₁ is the center of the first circle of the solution.
10. Construct a circle k₁ that is centered at S₁ and passes through point P. k₁ is the first circle of the solution.
11. Construct the line EQ. Name the intersection of the line EQ and the axis of the angle S₂. The S₂ is the center of the second circle of the solution.
12. Construct a circle k₂ that is centered at S₂ and passes through the point Q. k₂ is the second circle of the solution. Repeat steps 6-12 for points M, N, and K. Each of these repetitions gives us 2 solution circles.