Construction #4

To drop a perpendicular from a point to a line

Given a line and a point A not on the line

open the compass a distance larger than the perpendicular distance from the point to the line, and scribe an arc intersecting the line at two points.

Call the two points B and C. Scribe arcs from B and C of the same radius on the other side of the line from A.

Call the point where the two arcs meet D. Draw AD.

AD is the line through A perpendicular to BC.