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 ${\overline {AP_{1}}}$ and ${\overline {AP_{2}}}$

5. Construct the circle ${\overset {\frown }{AT}}$. 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 $P_2$