Use a compass to construct the perpendicular to line b from point A which is outside line b.
Construct your first circle with center A and radius AB. . (circle 1 black).Name the intersction between the circle and line given C.
Draw a new circle with center C through A.(circle 2-red)
Add circle 3(green) center B, through A. Mark the intersection of the red and green circles with D.
Join A and D , and you have your perpendicular.