Circle PPL

1. Begin with two points $$P_1$$ and $$P_2$$ and a line $$\overset{\leftrightarrow}{L}$$

2. Construct a line $$\overset{\longleftrightarrow}{P_1 P_2}$$. It intersects line $$\overset{\leftrightarrow}{L}$$ at point $$A$$

3. Construct the perpendicular bisector of $$\overline{P_1 P_2}$$

4. Construct the mean proportion of $$\overline{A P_1}$$ and $$\overline{A P_2}$$

5. Construct the circle $$\overset{\frown}{A T}$$. It intersects $$\overset{\leftrightarrow}{L}$$ at $$X_1$$ and $$X_2$$

6. Construct lines perpendicular to $$\overset{\leftrightarrow}{L}$$ that pass through $$X_1$$ and $$X_2$$. These lines intersect the perpendicular bisector at $$O_1$$ and $$O_2$$.

7. Construct the circles $$\overset{\frown}{O_1 X_1}$$ and $$\overset{\frown}{O_2 X_2}$$. These circles will be tangent to $$\overset{\leftrightarrow}{L}$$ and pass through $$P_1$$ and $$P_2$$