This construction can be used in place of the previous construction for passing a parallel line through an external point, but since it, like the first parallel construction, relies on tangent points it is less accurate and heavily dependent on practiced skill to accomplish a good representation.

Given a Right Line (AB) construct a second line parallel to Line AB that passes through Point P.

Using Point P as center, describe an arc of a circle that has a radius equal to the distance between Point P and Line AB. This arc should produce a tangent point on Line AB.

Select any point (D) on Line AB. Using Point D as center describe a second arc of a circle with a radius equal to the distance between Point P and Line AB that is on the same side of Line AB as Point P. Mark the point where the arc is farthest from Line AB as Point T.

Produce a line that passes through Point P and the second described arc of a circle at Point T. Point T, it should be noted, is the point where the produced line is tangent to the second arc.

The line passing through Points P and T will be parallel to Line AB.

~ An Instructive Animation Wherein the Foregoing Construction is Visually Explained ~