Hello, Joe!

Welcome aboard!

We are given three infinite straight lines.

We need to construct a circle that is tangent to the first two lines

and has its center on the third line. Code:

L2 / /
/ /
/ ♥ C
/ o /
/ o /
/ o /
/ o /
/ o / L3
/ o /
/ o /
/ o /
L1 / o /
- - * - - - - - - - - - * - - - - - -
/ /
/ /

Assuming that the lines intersect . . .

Construct the bisector of the angle formed by $\displaystyle L_1$ and $\displaystyle L_2.$

. . The center of our circle lies on this angle bisector.

Locate the intersection $\displaystyle C$ of the angle bisector and $\displaystyle L_3.$

. . $\displaystyle C$ is the center of the circle

Determine the perpendicular distance from $\displaystyle C$ to $\displaystyle L_1$ (or to $\displaystyle L_2$).

. . That is the radius of the circle.