How do you construct a tangent to a given circle and parallel to a given line?

Answer 1

There may be an easier way, but this is one way to do it:

1) establish the centerpoint of the given circle.

- pick two random points on the circle and draw intersecting arcs A1 A2 of equal radius centered on those points. Then draw a line through the two points where A1 and A2 intersect. This line will pass through the circle center.

- repeat with two other points. You now have two lines that intersect at the circle centerpoint C.

2) draw a line perpendicular to the given line that passes through C.

- draw an arc centered on C that intersects the given line twice. Repeat the bisecting procedure as before using those two intersection points. Call the newly created line L.

3) draw the desired tangent line.

- call the point where L intersects the given circle P. (Note that there are actually two such points, since there are two solutions to your problem - one on the near side and one on the far side.) Generate two equidistant points on L by drawing a small circle centered on P. Use those new points for the old bisection procedure and you have your answer!